Not all calculators are giving the same answer: Android - "undefined or +1" , Google and Windows - "-1"

An interesting thing to do is to use a good graphing calculator and graph the following: x^0, 0^x, and x^x and look at the graphed results. x^0 results in a line at 1 as you would expect. 0^x results in a line at 0 when x is greater than 0. x^x results in a very interesting shape.

@pedinurse1

10 ай бұрын

I dont see that at all

@ishansh0077

6 ай бұрын

x^x is non elementary

Woohoo! Working on almost 50 here. I loved math in school but I didn’t enjoy exponents. I currently feel like a genius for remembering and had the answer in just a few seconds before opening the video to see if I was right. 😂😂 Thanks for the self confidence boost!

@pedinurse1

10 ай бұрын

When did this rule come into being, that 0 is really minus one?? Must be the woke culture

@user-yb9ol8sz7o

7 ай бұрын

The product of zero zeros is undefined but can equal 1 or zero if mathematically necessary

@royreber526

4 ай бұрын

Back in grade school, we learned that "1/4" means that we are taking a whole pie and dividing it four ways equally. To say "1/0" means, " sorry, no division today!"

@marcelbastiaans8700

3 ай бұрын

Same here but I've passed the half century milestone.

Thanks for helping some of us overcome those feelings of shame, failure and dread we grew up with in math class all those decades ago. Truly a traumatic experience. "Heads, I win; tails, you lose." Nothing ever explained, nothing translated into English. Just a dismissive sneer and a lot of humiliating red ink. A game you couldn't win but had to keep playing. Every once in a while, I gather the courage to try to comprehend this bizarre and opaque system of thought. Why does 0 to the 0 power equal 1? "Because I SAY SO!" I'm hoping someday to understand what a "quadratic equation" is.

Training/ practicing for the IBEW aptitude test. your videos have been lots of help.

@jamesmilos9909

10 ай бұрын

Good luck on the test!

@mylittlepitbull3143

10 ай бұрын

Best of luck

-1? I know anything to the zero power is 1. Zero to the second power is 0. And zero to the zero power is 1. So 0-1 = -1.

@carultch

Жыл бұрын

Since you get contradictory results for x^y as x approaches zero, from what you get as y approaches zero, 0^0 is undefined, and not necessarily equal to 1. It is considered an indeterminate form, like 0 divided by 0.

@thomassicard3733

10 ай бұрын

Correct. Any other answer is bullsh*t.

@colej.banning2419

7 ай бұрын

That was my initial answer as well.

@SushilPaik-og2uv

5 ай бұрын

Please be informed that there is a condition in general, a^0=1 when "a" is not equal to "zero". So, the power of anything (here "a") is zero except a=0. Therefore, in this argument the result will be undefined.

@pulsar22

3 ай бұрын

I agree that Zero to Zero is 1. Here is proof. If x ^ 0 = 1 you cannot have 1 = nothing (since there is no x to multiply with). Therefore the form x ^ 0 = 1 is because x ^ 1 = 1 * (no x's). So 0 ^ 0 = 1 * (no zeroes) = 1

0 to the zeroth power is undefined no matter what, there's no opinions here, it's not humanitarian studies, math is precise . The property of x^0=1 is derived from the property a^m/a^n = a^(m-n), where we put m=n, but it is valid only if a≠0, because it is in the denominator of the LHS

So, out of two HPs and two TIs, all 4 give ERR (undefined). The only calculator I have the does otherwise is the Calculator program that comes with Windows!

@AlbertTheGamer-gk7sn

7 ай бұрын

At least the Windows calculator receives updates here and then, those calculators were stuck in the old era they were originally made with no updates ever since, so it couldn't keep up with the new defined numbers.

I was taught in the 1970s that 0 ^ 0 is undefined. You can't have nothing raised to the power of nothing, went the teacher's logic.

@thomass2451

6 ай бұрын

0^0 was undefined in the 1970s and is still undefined today. It will also be undefined in the year 3970.

@MuffinsAPlenty

6 ай бұрын

@@thomass2451 Except that 0^0 isn't undefined in pretty much any branch of discrete mathematics. When it comes to discrete mathematics, 0^0 = 1, and doing anything else (including calling it "undefined") just makes things unnecessarily complicated. (Depending on your definition of exponentiation, this is even sometimes _provable_ from the definition!) The decision by mathematicians in the early 19th century to un-define 0^0 (which was previously taken to be equal to 1, including by Leonhard Euler) is being recognized by more and more mathematicians as a mistake based on not properly understanding the concepts of limits and continuity. Because yes, the _only_ reason any mathematicians consider 0^0 undefined today is because of limits/continuity arguments.

@marcwilliams9824

6 ай бұрын

​@@MuffinsAPlentyOuch... :D

-1 0 squared is 0*0 + 0 to 0 power which is (1)=-1 it can also be undefined -

From another angle, 0^0 = 1 for the x^0 function. n^0 = 1, where n is negative real. p^0 = 1, where p is positive real. The x^0 function is continuous at x = 0. Using the x^0 function makes 0^0 = 1, which makes 0^2 - 0^0 = 0 - 1 = -1. Earlier, I used the 0^x function that makes 0^0 undefined and 0^2 - 0^0 undefined. Both solutions contradict each other. I don't know which "convention" to use, but favor the answer is Undefined.

I plug in smaller and smaller numbers for x in the expression x^x and it tends toward 1. However, if we approach 0 from the negative direction, my calculator responds with Error when I use small values. Oddly, my iPhone says (-2)^(-2)=0.25 instead of i*sqrt(2).

@arthur_p_dent

Жыл бұрын

your iphone is correct. i*sqrt(2) would be the square root of -2, which is equal to (-2)^(1/2), not (-2)^(-2).

@user-gp2wk8rz3p

6 ай бұрын

When x>0 , and even if x is not a hole number, x^x can be defined by exp(xln(x)). (You can try with your calculator for x=3, or x=2,5 for example). You can use this definition for exemple with 0,001 and you get 0,993...., but ln(x) is not defined for x

I still don't understand why 0 to the 0 power isn't 0. If I have 0 apples, no matter how many times I multipy no apples, it still comes out to no apples and you can't make a 3.14 with no apples.. And I don't need a calculater to figure this out. This is why I am 71 years old and never understood math - plus I hated it. Otherwise, I was mostly an A student. Math is just not rational, and in fact, all numbers just seem wholey irrational to me. That is why I choose to bake apples instead of counting them. Also, most of the people I know who do understand this are men. That is also why I don't understand men.......................I probably won't be back - I'm going to go bake an apple pie without counting how many it takes. Thanks anyway. P.S. I decided to come back just to give you a like, a 100%, a smiley face, an A++ and a few stars for trying since you seem to think it all makes sense and who am I to burst your bubble?

@BerndReinhardt

5 ай бұрын

Das rührt von einer Definition her, die besagt, dass jede beliebige reelle Zahl in der 0-ten Potenz immer 1 ergibt

@jackbettridge957

3 ай бұрын

It is actually undetermined. 0 to the 0 power could be anything because you are essentially dividing 0 by 0. In essence you asking what number times 0 equals 0, which could be any number.

@Wandjina104

3 ай бұрын

It's 1 or it can be classed as undefined. It's optional dependant on context. My answer was -1.

@mavrosyvannah

2 ай бұрын

​@@Wandjina104LOL...he thinks she wants an answer...you're the 👌

@vadim64841

Ай бұрын

0^0 can be interpreted as the limit of x^x where x -> 0, which can be proved to be 1. This video has missed golden opportunity to even mention, let alone explain, it. But then, again, this guy is well known for talking a lot while saying little …

I was average or worse at maths when at school. Now, in my 60s I seem to have improved significantly, having answered -1 within two seconds. However, I have never heard of undef as a result

@mylittlepitbull3143

10 ай бұрын

It takes patience to be good at math, so maybe you have more patience now.

@Llanchlo

9 ай бұрын

The more common undef is anything divided by zero

@franciscoedilbertoespinoza2662

5 ай бұрын

Un numero real o complejo al ser dividido por cero, el resultado se convierte en indeterminado o indefinido, como el caso del gringo bestia, que lo complica innecesariamente.

My Android phone calculator reports "Undefined or 1" for input "0^0". So I tried "0^0+5" and it still returns "Undefined or 1". Shouldn't it return "Undefined or 6"?

The calculator on my iPhone gives "Error" when I ask it to calculate 0^0. EDIT: my Casio fx-85GT PLUS also gives a "Math ERROR". But my spreadsheet app on my iPad (based on OpenOffice) gives 1. Although the Apple Numbers spreadsheet app gives an error message saying that 0 to the power 0 cannot be computed.

@AlbertTheGamer-gk7sn

7 ай бұрын

Those apps surely need a patch update, as 0^0 and 0! are equal to each other.

Loved that one just finished watching a criminal court case. Math and law are pretty similar. Numbers of great mathematicians were also lawyers.

@richardwilliamson1639

4 ай бұрын

That's because it's all arbitrary, arcane and handed down by others. The essence of authority.

@warrenstanford7240

4 ай бұрын

Both sets are embezzlers also 😆

As Don Benson put it, whether to define 0^0 is a matter of convenience not correctness. Many calculations get unnecessarily complex if we don't assign a value. And Don Knuth noted the real problem was we were comparing apples and oranges. 0^0 as a value is 1; 0^0 as a limiting form is undetermined.

@MiklosKoncsek

Жыл бұрын

The strange thing is...I do 0^0 on my windows calculator I get 1. BUT if I do this equation a different way - 0 divided by 0 - my calculator THEN gives me "result is undefined"

@b213videoz

Жыл бұрын

Orange is known as Applesin (son of apple) in some languages, both are fruits, both have comparable qualities - very easy to compare. Given enough intelligence one can compare anything 😁

@dougnettleton5326

10 ай бұрын

​@MiklosKoncsek, in what sense is 0/0 another way of 0^0?

@pedinurse1

10 ай бұрын

my calculator said zero

@cobbler88

9 ай бұрын

Cool. It doesn't change the answer, but cool.

First a word about 3^0, for example. We have 3^4=3^3×3, 3^3=3^2×3 and 3^2=3^1×3. If we want also to get 3^1=3^0×3, we have to take 3^0=1. This a choice, not a demonstration, but it’s often useful. We can’t do the same with 0^0, because to get 0^1=0^0×0, we can chose any value for 0^0. But what can we do? It’s not so easy, because it needs the functions exp et ln. For any real numbers x et n, with x>0, x^n can be defined by x^n=exp(nln(x). For example 3^2=exp(2ln(3))=9 et 3^2,1=exp(2,1ln(3))=10,045....... (we can’t do this with x0). Then we can observe that 0,1^0,1=0,794.... and 0,01^0,01=0,954.....and 0,001^0,001=0,993......For this reason, it seem’s to be a good idea to take 0^0=1. It’s a choice, often taken and which can be useful, not the result of a demonstration.

So, what if "all that" is part of a larger expression, as part of a larger physics problem? i.e. , What do I DO, with WHICH correct answer, as regards to associated expressions? OR ... How is which answer used, in a larger context?

@royreber526

4 ай бұрын

It means, "try something else. " Try using limits instead.

My old button calculator when using 0 X/y 0 it outputs 0. My phone using the same method outputs 1. To me, zero to the power of zero is zero.

@lookingforahookup

8 ай бұрын

Any number including 0 to the power of 0 is 1

@Astrobrant2

2 ай бұрын

To me, it's pointless, since I don't think there is any application for it. IOW, my answer would be "meaningless". It's like, "Where's the center of the surface of a sphere?" Or "What's farther north than the North Pole?" Or "What's infinity divided by 6?"

-1 If you're accumulating a sum, you initialize your accumulator sum to 0. Similarly, if you're accumulating a power, a number of multiplications of something, you initialize your "accumulator product" to 1. If you multiply it by something zero times, your accumulator is still 1. That's why logically 0^0 is 1. Added support for that is if you’re taking something to the 0th power, you’re multipling a starting value by it that number of times. “0” times means you’re multiplying by that number not even once, so that “0” doesn’t make it any different from any number to the 0th power. So you should get the same result as any other number to the 0th power is, namely “1”.

@10floz30minutes

10 ай бұрын

I agree with this.

@Nikioko

10 ай бұрын

And that is wrong. 0⁰ is undefined. You could argue that 0⁰ = 1 because x⁰ = 1, but you could also argue that 0⁰ = 0, because 0^x = 0. 0⁰ is undefined, the same way as x/0, log₀ and log₁ are undefined.

@10floz30minutes

10 ай бұрын

I did see it defined somewhere and before that it seemed strange to me too. Something about counting-principles or so...@@Nikioko

@cricri593

10 ай бұрын

by convention it makes 1 for continuity

@Nikioko

10 ай бұрын

@@cricri593 No. By convention, 0⁰ is ambiguous, and therefore undefined. You can say x⁰ = 1, but you can also say 0^x = 0. But here ist the reason 0⁰ is undefined: 0⁰ = 0² ⋅ 0⁻² = 0² ⋅ 1/0² = 0²/0² = 0/0. And devision by zero is undefined.

x^x, let x-> 0 from the negative side or from the positive side. You will get closer to -1 and 1. see also f(y)^f(x)) -- how you approach 0 matters. Some people have argued that 0 does not exist, it is just a very small number, maybe so small that if you square it you would get to nothing. 🙂 or 😲 -- the zero daemon.

@ManjulaMathew-wb3zn

5 ай бұрын

The limit as x->0- x^x =0 and from positive side it’s 1. So f(x)=x^x is discontinuous at x=0 and thus undefined.

Had a good chuckle with do not use a calculator. If ya don't know it's -1, not sure a calculator will help.

May be it helps to think about where a^0=1 comes! For example (a^5)/(a^5)=a^(5-5)=a^0=1 Here you have to write 0^n / 0^n = ? But before applying the formula n-n=0 and therefore 0^0 is 1, you must see that 0^n is 0 and that a division to 0 is undefined! 👍

@trwent

11 ай бұрын

You mean a division BY 0 is undefined.

@ft7339

11 ай бұрын

@@trwent Of course! 👍

@AlbertTheGamer-gk7sn

7 ай бұрын

Another thing: 0! is undefined as the factorial function is defined to be multiplication, and that (-1)! is infinity, and 0! = 0 * infinity... uh, oh...

5:15 in advanced mathematics 0^0 -can be interpreted as- *is* undefined. Let's emphasize that. I wonder whether the author of this video conducted any research beyond putting "0 ^ 0" in his calculator. Any sources? Is there any school book claiming the result is 1? *EDIT:* My claim was wrong. The result depends on the subject. For example, in discrete mathematics 1 is a sensible result. Thx MuffinsAPlenty.

@AlbertTheGamer-gk7sn

7 ай бұрын

But we need to define it. "Undefined" is just a code word of saying, "Screw this challenge. I'm turning back". This is very bad as it states that you are fearful and afraid of challenges. This is the exact opposite goal of humanity. Humans are meant to break away from nature using self-awareness, conscience, willpower, and imagination. This is why mankind managed to establish such civilization that sets them apart from all animals. We 21st-century humans must thank our long-gone ancestors by breaking away even more to make them proud. Einstein left in his will saying the first person that uses his theory of relativity to invent time travel must travel back to April 17th, 1955, to make him proud. "Undefined" is basically stating we are not used to those numbers, so let's just don't use them. It all depends on context. If we were living in Minecraft, a world without circles, and all of a sudden, a circle randomly appeared out of the blue, we would call it "undefined", but since in our world, we have polar coordinates, the premium package with the spherical bundle, we are accustomed to seeing circles, and we won't call them "undefined". Also, a long time ago, people worshipped the moon like a god at an "undefined" distance away from us, and they believed the sky's the limit, and everything they see in the night sky are basically pure celestial spheres of light at an "undefined" distance away from us, and the Earth was the point where those "undefined" distances converged to, but we managed to reach the moon and even send space probes outside our solar system, even attempting to reach the end of a universe, making such distances not "undefined" anymore. Finally, infinities are everywhere. Without it, the Big Bang wouldn't have happened, and every time you move, infinities are required to make it happen. Infinities created us, don't disrespect them by calling it "undefined" Divide by 0, spread your wings, learn how to fly, and do the impossible. We need infinities to make our dreams of time travel and superpowers come true.

@MuffinsAPlenty

6 ай бұрын

"in advanced mathematics 0^0 -can be interpreted as- is undefined." Depends on which subject you're dealing with. In basically all of discrete mathematics, 0^0 = 1 is correct. And this is because the empty product (a product with no factors) is 1. And the reason that the empty product is 1 is because that's the _only possible value_ a product with no factors could have if we expect a product with no factors to abide by the associative property of multiplication. In discrete mathematics, exponentiation represents repeated multiplication: x^n means a product with n factors, all factors being x. So, in discrete mathematics, x^0 means a product with 0 factors, all factors being x. In this context, regardless of the value of x, this is the empty product (the fact that all factors are x is _vacuously_ true, regardless of the value of x), and therefore, must have a value of 1. So pretty much any discrete setting, 0^0 = 1 is correct. And it actually shows up in formulas too (though you often wouldn't think to _use_ those formulas in those cases, which is why many non-discrete mathematicians don't notice this), and in every formula involving discrete exponentiation where 0^0 shows up, you _only_ get the right answer when 0^0 is evaluated as 1. And this makes sense because _everything_ about discrete exponentiation is based on the associative property of multiplication. Feel free to look up "empty product", although it belongs to a more general idea of "empty operation" which can be found in things like universal algebra and category theory. I recommend the article "too simple to be simple" on nLab, particularly the subsection on biased definitions. Now, in analysis things get a bit more sticky, and I'm happy to talk about that if you want, but I wanted to make the discrete case clear first.

@michaelmuller5856

6 ай бұрын

@@MuffinsAPlenty Thanks for the detailed and informative reply. To be honest, after wrting the comment I noticed that, for example, the binomial theorem (x + y)^n = x^0 * y^n + ... requires 0^0 = 1 to not break in the trivial case. Funnily enough, this didn't cross my mind during my studies. So, by now I would agree that 1 is "more correct" than 0 so to speak. What I'm wondering now: are there any areas (analysis) where people agree on 0^0 = 0? [The answer in this video ("the calculator says so") still feels a bit unsatisfying, but it's understandable he doesn't want to dive into advanced math to provide an example.]

@MuffinsAPlenty

6 ай бұрын

@@michaelmuller5856 "What I'm wondering now: are there any areas (analysis) where people agree on 0^0 = 0?" Not that I'm aware of. One time someone referred me to the concept of Munchausen numbers (or Münchhausen numbers - there ). A Munchausen number is a number where, if you take all of the digits in the representation of the number and raise them to themselves and then take the sum, you get the number back. So for example, 3435 is a Munchausen number since 3^3 + 4^4 + 3^3 + 5^5 = 3435. Obviously, Munchausen numbers are _super_ base dependent. Like 3435 is a Munchausen number in base ten but wouldn't be in other bases. *_Some_* people who have done work on Munchausen numbers adopt the convention that 0^0 = 0. For example, if one takes 0^0 = 0, then 438579088 is an additional Munchausen number in base ten. It's been proven that 0*, 1, 3435, and 438579088* are the only Munchausen numbers in base ten (* if one takes 0^0 = 0). Now, as you can probably guess, working on Munchausen numbers is a very fringe topic in mathematics, partially because it is not much more than a curiosity, it's super base-dependent, and then we get results which tell us that there really are only a few in any given base (so there isn't even much more that can be said about them anyway). But even in this fringe topic, taking 0^0 = 0 *isn't* agreed upon. For example, the person who named them "Munchausen numbers" to begin with says that the only two reasonable approaches are taking 0^0 = 1 or having 0^0 be undefined. (And in some bases, you get more Munchausen numbers when taking 0^0 = 1, as opposed to 0^0 = 0). But this is pretty much the _only_ situation I have seen where some people say taking 0^0 = 0 is what should be done. It's a fringe topic that seems uninteresting and arbitrary to me, and even those who have done work on this don't agree with that stance. In terms of analysis, typically analysts just take 0^0 to be undefined, and that's pretty much because of limits and continuity. The two-variable function f(x,y) = x^y cannot be made continuous at (0,0) even if one were to redefine 0^0. So that means some functions which have a limiting form of 0^0 will have a discontinuity associated with 0^0. And since analysts often want to deal with continuous functions, they will often take 0^0 to be undefined so that they don't have to deal with functions discontinuous at some point in their domains. Of course, there are _still_ plenty of situations in which they have to take 0^0 = 1, such as using power series/dealing with analytic functions. But still, I have _never_ seen an analyst suggest that 0^0 = 0 is "correct".

"0^0" is, by definition, not a number. It is a disallowed operation similar to division by 0, so it's use in an equation is disallowed. The equation is the equivalent of saying "What does 0^0 minus blue equal?"

@davidjenkins5776

3 ай бұрын

I strongly agree with you

When and where would you have this problem?

You could make 0^0 equal to any number between 0 and 1 if you try hard enough. For example, turn (0^0)/2 + (0^0)/2 into (\lim_{x\to 0} 0^x)/2 + (\lim_{x\to 0} x^x)/2 = 0/2 + 1/2 = 1/2.

My HP 11C (yes, it's older than you are, and still working fine) evaluates 0^0 as "ERR 0." So, I guess it subscribes to the "undefined" concept.

@robertakerman3570

Жыл бұрын

I've a TI 30. It began to melt(ha ha).

@coldlogiccrusader365

Жыл бұрын

I LOVE my HP 11C. I had one since 1974, lost it around 2002 and thank God found one in pristine condition on E-Bay. I guess it is the RPN, that spoils us. When forced to use any Non-RPN Calculator, it is a disaster. Before I watch further, I'm guessing he will use The Calculus, specifically the Limit of x^x as x->0 to prove 0^0 is undefined

@robertakerman3570

Жыл бұрын

@@coldlogiccrusader365 Define RPN. TYSM

@markgearing

Жыл бұрын

@@robertakerman3570 - Reverse Polish Notation. It’s a way of entering calculations without needing parenthesis. You enter the operands first, then the operator, so instead of (2+4)*(3+5)=, you’d key 2 ENTER 4 + 3 ENTER 5 + * So you get a partial result 6 when you keyed 2 ENTER 4 + and a partial result 8 when you keyed 3 ENTER 5 + and then the final result 48 when you keyed *

@robertakerman3570

Жыл бұрын

@@markgearing Europeans gave Us so much!

Why is 0^0 left undefined? Because you can find functions f(x) and g(x) such that f(x) and g(x) both approach 0 but f(x)^g(x) does not approach 1. For example, let f(x) = sin(x) and g(x) = 1/ln(x), where ln(x) denotes the natural logarithm of x. As x approaches 0 from numbers greater than 0, the given functions for f(x) and g(x) both approach 0. However, using techniques from Calculus II, we see that f(x)^g(x) is approaching e, which is approximately 2.718, rather than approaching 1. You can use your graphing calculator to help visualize the fact that, as x approaches 0 from numbers greater than 0, f(x)^g(x) is approaching e in this case.

@MuffinsAPlenty

7 ай бұрын

This is, indeed, the reason why mathematicians un-defined 0^0 in the early 19th century (prior to that point, mathematicians considered 0^0 to be equal to 1). But this argument _shouldn't_ be seen as convincing, at least when you think of 0^0 as an arithmetic expression, instead of as a limiting form. What I mean by this is: when we say 0^0 is an indeterminate form, we are not talking about the _number_ 0 raised to the power of the _number_ 0. Instead, we are talking about _a function approaching 0_ raised to the power of _a function approaching 0._ To me, an arithmetic expression is when we have operations between _actual numbers,_ and a limiting form is when we replace _functions with their limits_ in an attempt to avoid computing the actual limit directly. The next thing to note is this: it is perfectly consistent for the _arithmetic expression_ 0^0 to have a value of 1 while simultaneously the _limiting form_ 0^0 is indeterminate. This is because, if we go back to the meaning of limiting forms, 0^0 being an indeterminate limiting form simply means: "knowing f(x)→0 and g(x)→0 is insufficient information to determine the limit of f(x)^g(x)". And one of the key points about limits is that *_the limit of a function can be different from the value of a function._* Said in more symbolic terms, f(a) can be different from lim(x→a) f(x). *_If lim(x→a) f(x) always had to match f(a), then there would be no purpose to limits whatsoever._* But the argument that 0^0 is an indeterminate limiting form hence must be undefined as an arithmetic expression is essentially saying: "If f(a) is defined, then f(a) might not match lim(x→a) f(x), so we cannot have f(a) defined." Do you see the problem with this reasoning? It undermines the entire concept of limits. But even worse than that, I have never seen a natural example of a discontinuity _caused by_ 0^0 being defined as 1 (except for the situation where we have 0^f(x)). Even the example you gave is not a discontinuity caused by 0^0, but rather is a discontinuity caused by ln(0) being undefined and/or −∞ not being a number. Letting f(x) = sin(x) and g(x) = 1/ln(x), we do indeed get a limiting form 0^0 for f(x)^g(x) as x approaches 0 from the right. However, this is not the same thing as _plugging in_ x = 0. If we plug in x = 0, we get g(0) = 1/ln(0), which is undefined since ln(0) is undefined. If you _ignore_ the fact that ln(0) is undefined and pretend that ln(0) = −∞, then you still have the issue of g(0) = 1/−∞, which is undefined since −∞ isn't a real or complex number. If you _ignore_ the fact that −∞ isn't a real or complex number and pretend that 1/−∞ = 0, then you can conclude that g(0) = 0. But in order to conclude that g(0) = 0, you have to ignore the fact that ln(0) is undefined and ignore the fact that −∞ isn't a real or complex number. So the discontinuity of sin(x)^(1/ln(x)) at x = 0 is not the fault of 0^0, but rather the fault of 1/ln(x) being undefined at x = 0. Even if we defined 0^0 as e, sin(0)^(1/ln(0)) would still be undefined, by virtue of ln(0) being undefined. To reiterate, even if we defined 0^0 = e, sin(x)^(1/ln(x)) would still be discontinuous at x = 0, because sin(x)^(1/ln(x)) would _still be undefined at x = 0._ Therefore, we can see that 0^0 is not to blame for the discontinuity in sin(x)^(1/ln(x)) at x = 0, so claiming that sin(x)^(1/ln(x)) is an example of why 0^0 must be undefined as an arithmetic expression is just bad reasoning.

@AlbertTheGamer-gk7sn

7 ай бұрын

But we need to define it. "Undefined" is just a code word of saying, "Screw this challenge. I'm turning back". This is very bad as it states that you are fearful and afraid of challenges. This is the exact opposite goal of humanity. Humans are meant to break away from nature using self-awareness, conscience, willpower, and imagination. This is why mankind managed to establish such civilization that sets them apart from all animals. We 21st-century humans must thank our long-gone ancestors by breaking away even more to make them proud. Einstein left in his will saying the first person that uses his theory of relativity to invent time travel must travel back to April 17th, 1955, to make him proud. "Undefined" is basically stating we are not used to those numbers, so let's just don't use them. It all depends on context. If we were living in Minecraft, a world without circles, and all of a sudden, a circle randomly appeared out of the blue, we would call it "undefined", but since in our world, we have polar coordinates, the premium package with the spherical bundle, we are accustomed to seeing circles, and we won't call them "undefined". Also, a long time ago, people worshipped the moon like a god at an "undefined" distance away from us, and they believed the sky's the limit, and everything they see in the night sky are basically pure celestial spheres of light at an "undefined" distance away from us, and the Earth was the point where those "undefined" distances converged to, but we managed to reach the moon and even send space probes outside our solar system, even attempting to reach the end of a universe, making such distances not "undefined" anymore. Finally, infinities are everywhere. Without it, the Big Bang wouldn't have happened, and every time you move, infinities are required to make it happen. Infinities created us, don't disrespect them by calling it "undefined" Divide by 0, spread your wings, learn how to fly, and do the impossible. We need infinities to make our dreams of time travel and superpowers come true.

@AlbertTheGamer-gk7sn

7 ай бұрын

@@MuffinsAPlenty But we need to define it. "Undefined" is just a code word of saying, "Screw this challenge. I'm turning back". This is very bad as it states that you are fearful and afraid of challenges. This is the exact opposite goal of humanity. Humans are meant to break away from nature using self-awareness, conscience, willpower, and imagination. This is why mankind managed to establish such civilization that sets them apart from all animals. We 21st-century humans must thank our long-gone ancestors by breaking away even more to make them proud. Einstein left in his will saying the first person that uses his theory of relativity to invent time travel must travel back to April 17th, 1955, to make him proud. "Undefined" is basically stating we are not used to those numbers, so let's just don't use them. It all depends on context. If we were living in Minecraft, a world without circles, and all of a sudden, a circle randomly appeared out of the blue, we would call it "undefined", but since in our world, we have polar coordinates, the premium package with the spherical bundle, we are accustomed to seeing circles, and we won't call them "undefined". Also, a long time ago, people worshipped the moon like a god at an "undefined" distance away from us, and they believed the sky's the limit, and everything they see in the night sky are basically pure celestial spheres of light at an "undefined" distance away from us, and the Earth was the point where those "undefined" distances converged to, but we managed to reach the moon and even send space probes outside our solar system, even attempting to reach the end of a universe, making such distances not "undefined" anymore. Finally, infinities are everywhere. Without it, the Big Bang wouldn't have happened, and every time you move, infinities are required to make it happen. Infinities created us, don't disrespect them by calling it "undefined" Divide by 0, spread your wings, learn how to fly, and do the impossible. We need infinities to make our dreams of time travel and superpowers come true.

@MuffinsAPlenty

7 ай бұрын

@@AlbertTheGamer-gk7sn Please stop spamming this everywhere. You don't even read what you're replying to. You simply see something and decide to spam.

@AlbertTheGamer-gk7sn

7 ай бұрын

@@MuffinsAPlenty I'm just telling us that we should define the undefined, as that allows us to boost technological growth.

Always amazing to confront a limit to our total understanding in math or science. In time, what we think we know will change.

-1 I suppose one might verify that any number ^0 = 1 by exploring n^x as x->0 or limit as x ->0 i.e. x=0.1 =0.01 =0.001 =0.0001 say 5^x 5^0.1=1.175 5^0.01=1.016 5^0.001=1.002 5^0.0001=1.0001✔️✔️✔️ etc.... 0^0.1=0 0^0.01=0 0^0.001=0 0^1e-20=0 ???❌️ 0.1^0.1=0.794 0.01^0.01=0.955 0.001^0.001=0.993 0.0001^0.0001=0.999✔️✔️✔️ for n=0 revise the limits to n^x as n->0 and x->0 = 1

@CasaErwin

Жыл бұрын

But not ^zero or less. Zero to any power

I got the answer -1 without any confusion. However, even though I have a degree in mathematics, I was confused when you said that undefined was also correct. 😅 I guess I’d better grab my encyclopedia of mathematics and brush up a little bit. 😊

@Nikioko

10 ай бұрын

The answer -1 is incorrect.

@debbietroyer9480

10 ай бұрын

@@Nikioko I see that now, but I was still surprised by it. 😳

@gregorysagegreene

10 ай бұрын

I jumped to the chase without thinking and said 0, but when I saw your post I thought ... yeah.

@eemmeennddeell

9 ай бұрын

I have a degree in mathematics also and 0 to the 0 power is usually considered undefined.

@debbietroyer9480

9 ай бұрын

@@eemmeennddeell I believe it now. I’m not sure what I was thinking, but I confused myself. 🤨

Can you give me an example of any math question where 0^0 ever arises? Is there any practical application at all? IOW, what's the point of even discussing it?

The reason any number raised to the 0 power is 1 is because x^m/x^n = x^m-n. When you divide a number by itself, i.e., X^m / x^m that equals X^m-m or x^0, which is 1 because anything divided by itself is 1. That doesn't work for 0 though because 0/0 is undefined.

0⁰ in my calculator give "ERROR"... as it should. If you calculate lim Xˣ for x->0⁺, you'll get 1. But if you calculate lim 0ˣ for x->0⁺, you'll get 0. This ambiguity leads to the statement, that 0⁰ is undefined, as it depends on the situation.

@bobh6728

7 ай бұрын

Yes, it is undefined. A limit is not the same as a value you compute. The limit approaches 1 but it never reaches 1, so you can’t say the value is 1.

@AlbertTheGamer-gk7sn

7 ай бұрын

"Undefined" is just a code word of saying, "Screw this challenge. I'm turning back". This is very bad as it states that you are fearful and afraid of challenges. This is the exact opposite goal of humanity. Humans are meant to break away from nature using self-awareness, conscience, willpower, and imagination. This is why mankind managed to establish such civilization that sets them apart from all animals. We 21st-century humans must thank our long-gone ancestors by breaking away even more to make them proud. Einstein left in his will saying the first person that uses his theory of relativity to invent time travel must travel back to April 17th, 1955, to make him proud. "Undefined" is basically stating we are not used to those numbers, so let's just don't use them. It all depends on context. If we were living in Minecraft, a world without circles, and all of a sudden, a circle randomly appeared out of the blue, we would call it "undefined", but since in our world, we have polar coordinates, the premium package with the spherical bundle, we are accustomed to seeing circles, and we won't call them "undefined". Also, a long time ago, people worshipped the moon like a god at an "undefined" distance away from us, and they believed the sky's the limit, and everything they see in the night sky are basically pure celestial spheres of light at an "undefined" distance away from us, and the Earth was the point where those "undefined" distances converged to, but we managed to reach the moon and even send space probes outside our solar system, even attempting to reach the end of a universe, making such distances not "undefined" anymore. Finally, infinities are everywhere. Without it, the Big Bang wouldn't have happened, and every time you move, infinities are required to make it happen. Infinities created us, don't disrespect them by calling it "undefined" Divide by 0, spread your wings, learn how to fly, and do the impossible. We need infinities to make our dreams of time travel and superpowers come true.

@AlbertTheGamer-gk7sn

7 ай бұрын

@@bobh6728 But we need to define it. "Undefined" is just a code word of saying, "Screw this challenge. I'm turning back". This is very bad as it states that you are fearful and afraid of challenges. This is the exact opposite goal of humanity. Humans are meant to break away from nature using self-awareness, conscience, willpower, and imagination. This is why mankind managed to establish such civilization that sets them apart from all animals. We 21st-century humans must thank our long-gone ancestors by breaking away even more to make them proud. Einstein left in his will saying the first person that uses his theory of relativity to invent time travel must travel back to April 17th, 1955, to make him proud. "Undefined" is basically stating we are not used to those numbers, so let's just don't use them. It all depends on context. If we were living in Minecraft, a world without circles, and all of a sudden, a circle randomly appeared out of the blue, we would call it "undefined", but since in our world, we have polar coordinates, the premium package with the spherical bundle, we are accustomed to seeing circles, and we won't call them "undefined". Also, a long time ago, people worshipped the moon like a god at an "undefined" distance away from us, and they believed the sky's the limit, and everything they see in the night sky are basically pure celestial spheres of light at an "undefined" distance away from us, and the Earth was the point where those "undefined" distances converged to, but we managed to reach the moon and even send space probes outside our solar system, even attempting to reach the end of a universe, making such distances not "undefined" anymore. Finally, infinities are everywhere. Without it, the Big Bang wouldn't have happened, and every time you move, infinities are required to make it happen. Infinities created us, don't disrespect them by calling it "undefined" Divide by 0, spread your wings, learn how to fly, and do the impossible. We need infinities to make our dreams of time travel and superpowers come true.

@m.h.6470

7 ай бұрын

@@AlbertTheGamer-gk7sn there is philosophy and there is just plain dumb. This is in the latter category. "undefined" in this context simply means, that there is no unique answer for this question, but math requires a unique answer. Therefore it is "undefined", as - in the rules and axioms of math - this is unsolvable.

@AlbertTheGamer-gk7sn

7 ай бұрын

@@m.h.6470 Well, we humans find new ways to solve problems, as negative numbers, irrational numbers, transcendental numbers, and imaginary numbers are ways to make unsolvable problems solvable.

Zero to the zero power is undefined therefore it’s an illegal operation

so with one you need to pay attention to what ? is in this case its a variable so 0^2 - 0^0 = x

0^0=0 ( actually undefined but keep a chart going and you get help-=1^O-1 Then 0^0 = 1. Teferefore 0- 1 =-1

One reason I was behind in math, two answers to the same question that are totally different

@thomasw.eggers4303

11 ай бұрын

How about taking the square root of +1? There are two answers (+1, -1) that are totally different.

@ronnellmacklinJr

11 ай бұрын

@@thomasw.eggers4303 come again?

@witchy6978

10 ай бұрын

How about describing someone who is fat and ugly. Both fat or ugly would be correct.

@pedinurse1

10 ай бұрын

math has been twisted as they made up new rules

@thomasw.eggers4303

10 ай бұрын

@@pedinurse1 Hmmm. I used a computer in 1961 to plot a graph of x^x as x approached 0 from the positive side. The problem existed then as it still does.

0^0 is undefined therefore the answer is undefined.

@trannhatlong1968

Жыл бұрын

Right

@abhimanyubhattacharyya2403

11 ай бұрын

O^2=0 minus 0^0= undefined ,therefore for me the answer should be (0-- undefined)=undefined.

@AlbertTheGamer-gk7sn

7 ай бұрын

But we need to define it. "Undefined" is just a code word of saying, "Screw this challenge. I'm turning back". This is very bad as it states that you are fearful and afraid of challenges. This is the exact opposite goal of humanity. Humans are meant to break away from nature using self-awareness, conscience, willpower, and imagination. This is why mankind managed to establish such civilization that sets them apart from all animals. We 21st-century humans must thank our long-gone ancestors by breaking away even more to make them proud. Einstein left in his will saying the first person that uses his theory of relativity to invent time travel must travel back to April 17th, 1955, to make him proud. "Undefined" is basically stating we are not used to those numbers, so let's just don't use them. It all depends on context. If we were living in Minecraft, a world without circles, and all of a sudden, a circle randomly appeared out of the blue, we would call it "undefined", but since in our world, we have polar coordinates, the premium package with the spherical bundle, we are accustomed to seeing circles, and we won't call them "undefined". Also, a long time ago, people worshipped the moon like a god at an "undefined" distance away from us, and they believed the sky's the limit, and everything they see in the night sky are basically pure celestial spheres of light at an "undefined" distance away from us, and the Earth was the point where those "undefined" distances converged to, but we managed to reach the moon and even send space probes outside our solar system, even attempting to reach the end of a universe, making such distances not "undefined" anymore. Finally, infinities are everywhere. Without it, the Big Bang wouldn't have happened, and every time you move, infinities are required to make it happen. Infinities created us, don't disrespect them by calling it "undefined" Divide by 0, spread your wings, learn how to fly, and do the impossible. We need infinities to make our dreams of time travel and superpowers come true.

@AlbertTheGamer-gk7sn

7 ай бұрын

@@abhimanyubhattacharyya2403 But we need to define it. "Undefined" is just a code word of saying, "Screw this challenge. I'm turning back". This is very bad as it states that you are fearful and afraid of challenges. This is the exact opposite goal of humanity. Humans are meant to break away from nature using self-awareness, conscience, willpower, and imagination. This is why mankind managed to establish such civilization that sets them apart from all animals. We 21st-century humans must thank our long-gone ancestors by breaking away even more to make them proud. Einstein left in his will saying the first person that uses his theory of relativity to invent time travel must travel back to April 17th, 1955, to make him proud. "Undefined" is basically stating we are not used to those numbers, so let's just don't use them. It all depends on context. If we were living in Minecraft, a world without circles, and all of a sudden, a circle randomly appeared out of the blue, we would call it "undefined", but since in our world, we have polar coordinates, the premium package with the spherical bundle, we are accustomed to seeing circles, and we won't call them "undefined". Also, a long time ago, people worshipped the moon like a god at an "undefined" distance away from us, and they believed the sky's the limit, and everything they see in the night sky are basically pure celestial spheres of light at an "undefined" distance away from us, and the Earth was the point where those "undefined" distances converged to, but we managed to reach the moon and even send space probes outside our solar system, even attempting to reach the end of a universe, making such distances not "undefined" anymore. Finally, infinities are everywhere. Without it, the Big Bang wouldn't have happened, and every time you move, infinities are required to make it happen. Infinities created us, don't disrespect them by calling it "undefined" Divide by 0, spread your wings, learn how to fly, and do the impossible. We need infinities to make our dreams of time travel and superpowers come true.

@AlbertTheGamer-gk7sn

7 ай бұрын

@@trannhatlong1968 But we need to define it. "Undefined" is just a code word of saying, "Screw this challenge. I'm turning back". This is very bad as it states that you are fearful and afraid of challenges. This is the exact opposite goal of humanity. Humans are meant to break away from nature using self-awareness, conscience, willpower, and imagination. This is why mankind managed to establish such civilization that sets them apart from all animals. We 21st-century humans must thank our long-gone ancestors by breaking away even more to make them proud. Einstein left in his will saying the first person that uses his theory of relativity to invent time travel must travel back to April 17th, 1955, to make him proud. "Undefined" is basically stating we are not used to those numbers, so let's just don't use them. It all depends on context. If we were living in Minecraft, a world without circles, and all of a sudden, a circle randomly appeared out of the blue, we would call it "undefined", but since in our world, we have polar coordinates, the premium package with the spherical bundle, we are accustomed to seeing circles, and we won't call them "undefined". Also, a long time ago, people worshipped the moon like a god at an "undefined" distance away from us, and they believed the sky's the limit, and everything they see in the night sky are basically pure celestial spheres of light at an "undefined" distance away from us, and the Earth was the point where those "undefined" distances converged to, but we managed to reach the moon and even send space probes outside our solar system, even attempting to reach the end of a universe, making such distances not "undefined" anymore. Finally, infinities are everywhere. Without it, the Big Bang wouldn't have happened, and every time you move, infinities are required to make it happen. Infinities created us, don't disrespect them by calling it "undefined" Divide by 0, spread your wings, learn how to fly, and do the impossible. We need infinities to make our dreams of time travel and superpowers come true.

I think it more correct to call it indeterminate than undefined.

At 7:38, it mentions 7/0 is undefined. But it seems like the answer would be infinity. Like zero would go into any number an infinite number of times.

@shanonatwater8752

7 ай бұрын

Any number divided by 0 is undefined, but it also is said to approach infinity. Math is weird at times

@nekogod

6 ай бұрын

Infinity is not a number and can't be treated as such. If you say 7/0 = infinity then you could also say that 3/0 = infinity which leads to the contradiction that 0*infinity = both 3 and 7 or written another way 7/0 = infinity = 3/0 which becomes 7/0 = 3/0, multiply both sides by 0 and you get 3 = 7 which is obviously nonsense.

For any nonzero number a, a^0 = 1. The power 0^0 is undefined.

@firstname4337

9 ай бұрын

Zero to the power of zero, denoted by 0⁰, is a mathematical expression that is either defined as 1 or left undefined, depending on context. In algebra and combinatorics, one typically defines 0⁰ = 1. In mathematical analysis, the expression is sometimes left undefined. -- wikipedia

@AlbertTheGamer-gk7sn

7 ай бұрын

"Undefined" is just a code word of saying, "Screw this challenge. I'm turning back". This is very bad as it states that you are fearful and afraid of challenges. This is the exact opposite goal of humanity. Humans are meant to break away from nature using self-awareness, conscience, willpower, and imagination. This is why mankind managed to establish such civilization that sets them apart from all animals. We 21st-century humans must thank our long-gone ancestors by breaking away even more to make them proud. Einstein left in his will saying the first person that uses his theory of relativity to invent time travel must travel back to April 17th, 1955, to make him proud. "Undefined" is basically stating we are not used to those numbers, so let's just don't use them. It all depends on context. If we were living in Minecraft, a world without circles, and all of a sudden, a circle randomly appeared out of the blue, we would call it "undefined", but since in our world, we have polar coordinates, the premium package with the spherical bundle, we are accustomed to seeing circles, and we won't call them "undefined". Also, a long time ago, people worshipped the moon like a god at an "undefined" distance away from us, and they believed the sky's the limit, and everything they see in the night sky are basically pure celestial spheres of light at an "undefined" distance away from us, and the Earth was the point where those "undefined" distances converged to, but we managed to reach the moon and even send space probes outside our solar system, even attempting to reach the end of a universe, making such distances not "undefined" anymore. Finally, infinities are everywhere. Without it, the Big Bang wouldn't have happened, and every time you move, infinities are required to make it happen. Infinities created us, don't disrespect them by calling it "undefined" Divide by 0, spread your wings, learn how to fly, and do the impossible. We need infinities to make our dreams of time travel and superpowers come true.

Just a thought. I know 0^0=1 but I’d love to see the mathematical proof of this. That be interesting.

@arthur_p_dent

Жыл бұрын

You could define it as 1 because the limit of a^0 for a towards 0 is 1. Then again, you could define it as 0 because the limit of 0^x for positive x towards 0 is 0. At the end of the day, 0^0 is just as undefined as 0/0 or 0*infinity.

@TheloniousCube

10 ай бұрын

@@arthur_p_dent At the end of the day it's defined as 1

@arthur_p_dent

10 ай бұрын

@@TheloniousCube at the end of the day, this is a matter of convention. You can define it as 1, or not.

@TheloniousCube

10 ай бұрын

@@arthur_p_dent In the context of algebra mathematicians define it as 1

@davidloewen5528

10 ай бұрын

It is a definition, not a proof. As such it is somewhat useful, sort of like i=✔️-1

-1. Y^Y based on limits as Y approaches infinity. 0-1. I am guessing.

Consider that X^0=1 but 0^X = 0. Combine the two and that should tell you that you dont know if 0^0 is 1 or 0. In fact if I try to do 0^0 on my TI-85 it gives me a domain error.

You can’t subtract by something that is undefined.

@awcabot1

Жыл бұрын

The RULE is that any base elevated to the zero power = 1. Therefore, it’s NOT undefined because it’s already defined by the rule.

@mjsteele42

11 ай бұрын

​@@awcabot1 False. The rule says that any NONZERO base raised to the zero power is one. A power of zero is not defined for a base of zero.

@Covid-Covid--xo3ok

11 ай бұрын

X⁰ = 1, (X # 0.)

@TheloniousCube

10 ай бұрын

but 0^0 IS defined

@dioniciotorres4290

10 ай бұрын

I agree with you in principle but since they are defining 0 exponent as 1. Maybe he should have put that in the question.

This is (I hope) just a case of remembering that Zero to the power Zero is 1 Zero to any other power is Zero. So, we have Zero squared - Zero to the power Zero 0 - 1 = - 1 EDIT (after watching your video) I still don't quite get how an equation can have an answer and be 'undefined' as well.

@BAM-jc7uy

9 ай бұрын

👍

The calculator my iPhone returns “Error” when I attempt to raise 0 to the power of 0. Other numbers raised to the power of 0 = 1.

@AlbertTheGamer-gk7sn

7 ай бұрын

Steve Jobs died, so he couldn't fix that bug. Maybe, his ghost can use supernatural power to fix the bug magically in the future.

How can anyone gets it wrong? And when you say "a lot of people..." where did you get that statistics?

0^0 is generally undefined. The most common is to set it to 1 so that x^k evaluates to 1 for x=0 and k=0 in a sum or series. But one may set it to anything suitable for the case where it's used. So all of the three alternatives, as well as any other answer, is actually correct.

how can 0 become -1 when if you have no money and empty pockets than logic says you have nothing

@mcsmith732

10 ай бұрын

Debt?

@pedinurse1

10 ай бұрын

totally agree

Ok, Ok. What I want to know is which Gray Beard was able to sell this definition? When will he die, and when will the new Gray Beard change the definition? What will A.I. say?

I'm guessing -1, since any number to the ⁰ is 1. Don't know if that tile works for 0.

Undefined to me means that there is no answer or it is irrelevant because it can't be answered so its return is equal to 0. I still see the answer of 0 being valid.

@davekearney1944

9 ай бұрын

Here's an experiment - take a pencil and do the following division ---- 7 ÷0. See what you get.

@tervalas

9 ай бұрын

Dave needed to add more context to show why 0 isn't an answer. Think of why x^0 is always one. For example, 2^2 divided by itself. Which is 4/4 which is 1. Using power laws, you subtract exponents when dividing, so you get 2^0. But we already know the answer is one, therefore 2^0 has to be equal. When it comes to a 0 base, and you do the same process, you get 0/0, and we know division by 0 can't be done, therefore it cannot be an answer. Now, if you are approaching your comment from a logic standpoint, with 0 as a return value for anything that isn't true, I can understand your thought. But this isn't a logic problem, and 0 in math isn't a replacement for 'undefined'.

@anthonywarfield7348

8 ай бұрын

Undefined is basically saying we humans don't have the intelligence to comprehend this. Nature however does it every time a black hole is created. Nature also has no problem with irrational or complex numbers. A perfect circle should be impossible because it is a ratio of its circumference and radius, i. e. it is a product of pi . Pi is irrational though and cannot be described as a ratio. So what gives. We do, and we know it. That's why concepts like undefined exist. We don't have the knowledge to describe it yet. I hope this helps.

@davekearney1944

8 ай бұрын

@@anthonywarfield7348 You don't give humankind nearly enough credit for our understanding of certain basic mathematical concepts. Re - Perfect circle. Pi is indeed an irrational number which means, as you point out, it can't be expressed in the form of a ratio of integers. Basically it can't be expressed as a fraction. But the value of Pi is not in any way required to express the equation for a perfect circle. The value of a circle (simplified to locate the center at origin) is x^2 + y^2 = r^2. Pi is not required. You could, however, support an argument that the numerical value of the area of circle (or volume of a sphere) cannot be "perfectly" calculated due the irrational value of Pi. Re - "Undefined". We should come up with another term for that because it sounds like it means "geez, I dunno and might never know!". We understand the concept, or concepts. There are several ways an expression can result in an "undefined" solution. That's important - numbers can't be "undefined", only expressions can be "undefined". So what's the problem with division by zero? Let's use an example- 10 ÷ 5 = 2. We can check that by recognizing 2 × 5 = 10. Let's try that with division by zero. 10 ÷ 0 = y therefore y × 0 must equal 10. There is no solution for that expression. There's no number which can be multiplied by zero to equal 10. The answer is "undefined". We fully understand that. There's no mystery.

@antifascistnetwork4137

8 ай бұрын

It doesn't say thr equation is undefined. The andwer is -1

-1... Yay!... I'm in the 30%....

Is it like the inverse of dividing by zero?

To get a number to the zero power start with that number to any power and divide it by the same number to the same power. The answer is always 1. e.g. a to the n divided by a to the n = 1 ( how many a to the nth in a to the nth?). The problem is that when applying this to zero we are dividing by 0 which is a no no. I have a "proof" that 1=2. Guess where the mistake is hidden.

I could not believe that a calculator would return 1 for 0^0. This is the same as 0 divided by 0 and you cannot divide by zero. The only proper answer is undefined. So, I put it into my calculator and it gave an error, which is what it gives for any other division by zero.

@daniellitton4764

Жыл бұрын

In what universe is..x-0 the same thing as x÷0??? -1 is absolutely a correct answer.

@taknothing4896

Жыл бұрын

I just for fun tried 0^0 on the rp calculator on my desktop, and it gave 1, which is just what I thought at first. However, I can also guess that it might be represented by a transfinite number, just as x/0 if I'm not getting totally confused of course.... Anybody wanna step in and enlighten me?

@anwaraisling

Жыл бұрын

No, 0^0 is not equivalent to 0/0. Who taught you that? I’d like to remove their license.

@thomasaquaball4864

11 ай бұрын

He ist right: 0^0 = 0^(1-1) = 0^(1)*0^(-1) = 0^1 / 0^1 = 0/0 Division by 0 i not forbidden, just simply UNDEFINED. (As long as you are not using 'limits'.) The video ist just wrong!!

@TheloniousCube

10 ай бұрын

0^0 is defined as 1

0 to the power of 0 is undefined

@anwaraisling

Жыл бұрын

Not necessarily. It has long been taught that any number ‘x’ raised to the power ‘0’ (so x^0) is 1 algebraically. Therefore, when x=0’ 0^0 = 1. Remember, this is just standard convention. There are often special use cases that go against standard convention, which is why PEMDAS does not hold true for algebraic division. In such cases, everything after the division goes under the division dividing everything before the division. It is for this reason that undefined can also be correct under specific circumstances.

@Ivan-fc9tp4fh4d

Жыл бұрын

@@anwaraisling No. It is undefined, because it leads to the expression 0 / 0.

@TheloniousCube

10 ай бұрын

@@Ivan-fc9tp4fh4d No, it is defined as such. "It leads to..." is not a valid argument

@Ivan-fc9tp4fh4d

10 ай бұрын

@@TheloniousCube 0 . 0 - 0^0 = 0 - 1 = -1 ?

@Ivan-fc9tp4fh4d

10 ай бұрын

@@TheloniousCube Zero to the power of zero, denoted by 0^0, is a mathematical expression that is either defined as 1 or left undefined, depending on context. In algebra and combinatorics, one typically defines 0^0 = 1. In mathematical analysis, the expression is sometimes left undefined. Computer programming languages and software also have differing ways of handling this expression. And that's why some missions to Mars CAN CRASH ... :) Beacuse of different DEFINITIONS ...

Consider 0^5/0^5. Applying the rule ‘when you divide like bases you subtract their exponents’ you would get 0^(5-5) or 0^0. Since division by 0 is undefined 0^0 is also undefined. Not 1.

Ok the fact is that zero to the power of zero is sometimes defined as 1 (good arguments see Donald Knuth) to catch some special cases in polynoms or eg the geometric sum formula or the binomic formula and in calcus it is undefined because the limit is not defined see the statement from french math. Cauchy. So sometimes it is practical to define it ans sometimes it is not, it is the decision of the programmer of a cas or calculator program and there is absolutly nothing wrong with it

This is all wrong from the start. The answer -1 is wrong. 0^0 is undefined. When you say x^0=1 this is true for any x different than 0. Proof: x^2 = x^(2+0) = x^2 * x^0. So if x^2 is non zero divide both sides by x^2 and obtain x^0=1. Now x^2 is different than zero as long as x is different than zero. So we proved that x^0=1 if x different than 0. If x=0 funny things can happen. This will depend on how fast you go close to 0. The result can be 0, infinity or a finite number. Second point: my calculator gives 0^0 as an error. I used the scientific calculator on my iPhone. Thirdly, please do nit encourage people to use the calculator blindly. This is so bad practice. Learn the concepts of mathematics. A calculator is just a machine, your brain can think.

@TheloniousCube

10 ай бұрын

0^0 is defined as 1

@AlbertTheGamer-gk7sn

7 ай бұрын

But we need to define it. "Undefined" is just a code word of saying, "Screw this challenge. I'm turning back". This is very bad as it states that you are fearful and afraid of challenges. This is the exact opposite goal of humanity. Humans are meant to break away from nature using self-awareness, conscience, willpower, and imagination. This is why mankind managed to establish such civilization that sets them apart from all animals. We 21st-century humans must thank our long-gone ancestors by breaking away even more to make them proud. Einstein left in his will saying the first person that uses his theory of relativity to invent time travel must travel back to April 17th, 1955, to make him proud. "Undefined" is basically stating we are not used to those numbers, so let's just don't use them. It all depends on context. If we were living in Minecraft, a world without circles, and all of a sudden, a circle randomly appeared out of the blue, we would call it "undefined", but since in our world, we have polar coordinates, the premium package with the spherical bundle, we are accustomed to seeing circles, and we won't call them "undefined". Also, a long time ago, people worshipped the moon like a god at an "undefined" distance away from us, and they believed the sky's the limit, and everything they see in the night sky are basically pure celestial spheres of light at an "undefined" distance away from us, and the Earth was the point where those "undefined" distances converged to, but we managed to reach the moon and even send space probes outside our solar system, even attempting to reach the end of a universe, making such distances not "undefined" anymore. Finally, infinities are everywhere. Without it, the Big Bang wouldn't have happened, and every time you move, infinities are required to make it happen. Infinities created us, don't disrespect them by calling it "undefined" Divide by 0, spread your wings, learn how to fly, and do the impossible. We need infinities to make our dreams of time travel and superpowers come true.

It seems to me that zero is an easy answer, right?😢 I wish someone could explain logic behind nothing with no power can be something.

@pedinurse1

10 ай бұрын

exactly

@doseofsanity

8 ай бұрын

Yeah, try doing it with apples and see how many apples you end up with, zero.

@aldrikvoldus585

8 ай бұрын

It deals with sets of numbers. If you had 0 apple trees that produce 0 apples this year there is only 1 way you get this result.

@AlbertTheGamer-gk7sn

7 ай бұрын

0!: Am I a joke to you?

Based on the rule w/c says: Any # except zero raised to the power zero is one, Hence 0 raised to the zero exponent is definitely not 1.

Why is one 'power' & the other 'square' with same placements? TIA

69 y.o. mechanical engineer. -1 all day long.

@ajabkhan9320

Жыл бұрын

Ajab khan khattak.What about night sir?

@vespa2860

Жыл бұрын

@@ajabkhan9320 It's sleeping.

Zero to power zero is undefined therefore the answer would be 0

@robertakerman3570

Жыл бұрын

Yah, I'd go w/that.

@anthon3373

Жыл бұрын

No.. base on ur logic 0 to power of 0 is undefine then ur ans will be undefine. For me 0^0 is 1 according to the rule

@anwaraisling

Жыл бұрын

No, algebraically x^0 is defined as 1. Therefore 0^0 is 1. However, this is not the only convention that algebra varies. Algebra doesn’t follow PEMDAS. When applying division, algebra divides everything that comes before the division by everything that comes after the division. As with a lot of math, it depends. Which is why both 1 and undefined can both be correct leading to -1 in this case.

@carultch

Жыл бұрын

@@anwaraisling Where do you get the idea that "Algebra doesn't follow PEMDAS"?

@alexaneals8194

Жыл бұрын

@@anwaraisling You have to realize that raising to the zero power means dividing the number by itself. 0/0 is undefined. 10/10 = 1 so 10 raised to the zero power equals 1.

If 0^0=1 because a^0=1 for any other a, then why is 0/0 undefined even though a/a=1 for any a other than 0? Also, 0^(1/n) = 0 for all n=1,2,3... , converging to 0^0=0. It may make sense to set 0^0=1 in many instances, but there are exceptions. Thus, undefined. btw, using the usual exponential law x^(a+b) = x^a * x^b, we could consider: 0^0 = 0^(0+0) = 0^0 * 0^0 thus, 0^0 must be some a that satisfies a=a^2, leading to exactly two solutions, 0^0=0, or 0^0=1.

@MichaelRothwell1

11 ай бұрын

Re why is 0/0 undefined even though a/a=1 for any a other than 0: this is good question. Remember that division by a number is the operation that "undoes" multiplication by that number. For example, 3×2=6, so 6÷2=3. Written in the opposite order, 6÷2=3, so 3×2=6. In general, a/b means the number you must multiply by b to get a. In symbols, a/b=c means that c solves c×b=a. To work out a/a, we put b=a to get: a/a=c, where c solves c×a=a. Now if a≠0, we can divide both sides of the equation by a to get c=1, and we're done. If a=0, the equation becomes c×0=0, and this is satisfied by any real value c. So in a sense 0/0 can take any real value. Because 0/0 doesn't have a definite value, we say that it is undefined.

Interesting to do on a Reverse-Polish notation calculator like I always use. (Ancient HP65).

First comment!!! 🎉

@robertakerman3570

Жыл бұрын

WooooHoooo!

Before calculators when I was at school it was 1 so do as I had to and use reams of paper and a biro Or as when I was in primary a pen with hib and a full ink well

-1 as in the rule of power anything to the power of 0 is 1 so 0 - 1 is -1

Mathematics is a mix of logical operations and conventions. n^0 = 1 by convention and this applies to 0^0.

I got -1 right off the bat , and then dove into the comments to see ALL the arguments, lol 😅

My answer was -1. My scientific calculator on my mobile says: underterminate. If I remember it correctly anything raised to power 0 is defined to be 1, because that conforms to the rules of addition of exponents. I watched the video just to be reminded of what I learned in math 50 years ago. But it's easy to see why 0^0 has to be defined to 1.. How anyone can think it's undefined baffles me, though. That would create some havoc!

X high 0 IS per definition for every natural number 1, afaik. So the result should bei -1. Written before watching the Video.

I'm gonna say "it depends". But 0^0 = 1 looks seems good unless it needs to be something else. So either "-1" or "undefined".

I hadd 0 and undef. Zero to the zero'th power is the same as 0 times 0? How the heck can nothing become 1? Would you come to the same result without a calculator?

bro will never run out of vid ideas lmao

Please explain HOW any number to the zero power is 1. This seem to me that you simply had know what the that rule is and the rest would be easy. Please some one show me a proof?

This becomes 0-1= -1. (This is based on the rule x^0 is 1, though I believe in the case of 0^0 it can be 1 or undefined).

@nekogod

6 ай бұрын

Yeah but 0^x is 0, so 0^0 has to be both 1 and 0 at the same time. Which is nonsense so undefined is really all it should be.

isn't any number raised to the 0 power equal to 1?

@themister3865

4 ай бұрын

I seem to recall one of my college math professors proving this rule longhand on a chalkboard back in the early 1970's.

Yo pensé en 1 pero olvidé el signo de (-) pero yo no sé por qué intuí por lo pronto qué 0 elevado a la 0 era 1. No sabia la respuesta, sólo lo intuí.

I remember that any number to the 0 power is 1. The question is whether this applies to zero. If so. then answer is -1. Otherwise equation is invalid.

-1. Zero to the power of anything except zero is zero. Anything, even zero, to the power of zero, is 1. Zero minus one is -1.

Any real number to the zeroth power equals 1. That's the rule. Just like PEMDAS is the rule. Zero times zero is zero. Zero minus 1 is negative 1. It's not that complicated. However, in a more philosophical environment, is zero actually a number, or is zero a null set. One, two, three, etc are values. Is zero a value or is it just nothing.

I studied advanced math at UCD before we had calculators and I got good grades. My grandson is smarter than me and he is struggling with math at UCSB. What have you professors done to make math complicated like you show in your video?

my gut instinct was to say the result is zero but then i thought about 0^0 for a bit and ended up at undefined. I couldn't see how an equation with only zeros resolves to a number that is not zero because that just didn't make any sense in my head. So undefined was my answer in the end. I bet calculators simply have the rule that ^0 is always 1 with no exception for 0^0.

@craigthomas2497

6 ай бұрын

You are correct about calculators.

ZERO was my guess. but now understand that 0 to the power of 0 = 1, so -1 would be my answer. Thanks!!!

I said 0. But I either did not remember the rule about 0 =1 and undef is 0. Unless we are going to translate terms into numbers. Still fun anyway. Even -1 times 0 is 0. But you the boss and probably right

There is another reason why I say it’s undetermined. Let’s assume 0^0=1. If it’s defined like that I will perform legal mathematical operations on it to create a contradiction. 0^(1-1)=1 (0^1)(0^(-1)=1 (0^1)/(0^1)=1 0/0=1 and that’s a contradiction. Assuming 0^0=1 all operations I performed are valid but they led to an undefined result. That means the original assumption is incorrect.

x^0 comes from x^a/x^a => x^(a-a) -> x^0 BUT! 0^0 would then come from 0^a/0^a -> 0^a/0 -> division by zero -> undefined

Explain how you calculated 75% please.

The binomial theorem: (a + b)^n=... would collaps for the case where b = 0 if 0^0 wasn't DEFINED to be = 1.❤

@quincyberman5629

6 ай бұрын

PEMDAS is your friend

When did zero times anything not equal zero?

You broke my brain when you wrote 0^0 power 😆 when i see indeterminate problems, my brain says no no no that doesnt work 😆

My RPN calculator returns "Error" when I enter 0⁰

@AlbertTheGamer-gk7sn

7 ай бұрын

Too bad your calculator doesn't update!