I love your enthusiasm!

I didn't recognise this "floor" notation and thought you were asking me to find the continuous integral of x dx between 0 and 1. Interesting problem with an interesting result, though.

Glad I got it right. Euler's solution to the Basel problem is a fun topic by itself. I love it when continuous and discrete domains are mixed. Reminds me of signal processing math.

Great video!

Very cool solution - thanks 👍

Very cool!

Great video! Vear clear explanation, and a cool final result. If you want a challenge, you could try: Integral from 0 to infinity of {e^x} - 1/2 i.e fractional part of e^x, subtract 1/2

No it had me on the "ceiling"!

Great video as always! I am pretty sure that the last integral, of the frational part of {1/x} from 0 to 1, is actually positive and equal to 1-gamma. I transfered the integral to a pretty weird sum, and as wolfram alpha said, the sum equals 1-gamma.

Thank you so much ❤

Any math problem will have me on the floor in a fetal position

The last integral is positive: 1-γ.

I accidently discovered what a floor function was trying to find the wave equation of a triangular traveling wave. It scared me and so does this integral.

Perfect❤❤ i love your show

Hi PROF nice to see U back☺

Fun math, fun video and fun guy.

very good video, it could help me to solve an integral with matrices or with linear algebra, greetings from Mexico

WTF happened to the floor.

@tyruskarmesin5418

Жыл бұрын

Floor is the piecewise function that let him break it into a bunch of simple integrals.

@aneeshsrinivas9088

Жыл бұрын

I was making a pokemon talk reference.

@yogi30051972

Жыл бұрын

​@@tyruskarmesin5418 can you give more info on this please? I'm new to these functions. I looked it up on wiki but it described it in a very strange way and I don't understand

@adrienanderson7439

Жыл бұрын

​@@yogi30051972 ​So for each interval of x that he integrates 1/x over, (1/2 to 1 and 1/3 to 1/2 ect), the floor of 1/x for x being in that interval is just a constant. For example 1/x where x is a value somewhere between 1/3 and 1/2 means 1/x is between 2 and 3 so the floor of 1/x is just 2 (decimal part removed). Which allows him to integrate the floor of 1/x as just 2 over that interval. If you add all those pieces together you get the whole integral from 0 to 1.

@Djdjennerd

Жыл бұрын

memory unlocked

I derived the series at 1:47 using integral substitution. If we let u=1/x, then dx = 1/u du (note I didn’t mix up x and u here, the two formulations are equivalent). From there it’s a relatively straightforward forward sum of integrals.

I literally just saw this problem on Brilliant yesterday and thought... "Huh!? Where do I even begin??" Thanks.

The integral of the integer part does not necessarily need to be an integer because the integer part is just in the integrand correct and it becomes an infinite series as we saw what you did. - Good to see Euler Mascheroni constant again!

I felt smart when I figured this out without watching the video, then I felt even smarter after reading the comments lol!

@jameeztherandomguy5418

Жыл бұрын

bruh look at the thumbnail its not the floor f unction there, so people solved it on the thumbnail

Always looks like there is something mysterious when we manage integer numbers and suddenly appears Pi

Doubly cool!

That right-hand expression collapses like a cheap suit.

The calculation you did in the video uses the floor function, which is different from the image shown in the thumbnail

@drpeyam

Жыл бұрын

The thumbnail shows the floor function

@a.b.c.d.e...

Жыл бұрын

​@@drpeyam the Thumbnail shows square brackets

@maitri1656

Жыл бұрын

@@a.b.c.d.e... Greatest integer function

@johnloony68

Жыл бұрын

No it doesn’t. The thumbnail shows square brackets [ ]

@drpeyam

Жыл бұрын

It’s another notation for the floor function…

My face in the floor when doctor peyam make a video ❤😊

@drpeyam

Жыл бұрын

Awwwwww thank youuuu!!!

Amazing 🥰🥰🥰🥰

I must be missing something. Isn't [1/x]expn(-1) just x? So that would be Integral(x) from 0 to 1. And wouldn't that just be 1/2?

@drpeyam

Жыл бұрын

No it’s the floor function

Beautiful result out of ugly integral 😂

After reading the comment section I am convinced that a lot of people, even in the math community, don't know what the floor function is.

@drpeyam

Жыл бұрын

I know right?? I’m so shook 😂

@jameeztherandomguy5418

Жыл бұрын

@@drpeyam thumbnail doesnt CONTAIN it

@thegrandmuftiofwakanda

Жыл бұрын

I've used it a lot over 20+ years in MATLAB / C / C++ where we just see it as floor() but have never seen this "partial square bracket" notation.

@thegrandmuftiofwakanda

Жыл бұрын

@@jameeztherandomguy5418 Yes that's why I thought the problem was to integrate x dx between 0 an 1, which of course is trivial. Then on the white board it looks different, if you spot it.

@softwarelivre2389

Жыл бұрын

People do know what the floor function is. The problem is the thumbnail did not show the floor function.

What about studying the triples as [2,3,5] with one even and two odds numbers such that 2*3+5=11 (prime); 2*5+3=13 (prime); 3*5+2=17 (prime) ? Never heard about this topic. Seems quite interesting excluding symmetries. Another example could be [3,7,10] ... and so on and so forth...

@drpeyam

Жыл бұрын

I’m not a number theorist

how is that second sum telescoping? Did you mistake it for the sum of (1/n - 1/(n+1)) or did I miss something?

@drpeyam

Жыл бұрын

It is telescoping, you can use partial fractions

@decare696

Жыл бұрын

Aaah I see, the numerator is 1 + n - n.

(1/x)-¹ = x

@curtiswfranks

Жыл бұрын

But not if there is a floor in the middle.

Pi squared? No way! Pi are round. Cornbread are square.

@buddydog1956

Жыл бұрын

Pie a la mode ~

@lorax121323

Жыл бұрын

Potato casserole squared

great

Fun video!

i initially got confused with the floor functions, but then i realised it is actually the least integer function (thats what we call it in india) and your ceiling function would be Greatest Integer Function

@vask5500

4 ай бұрын

It's the other way around. Floor is the greatest integer function

I'm from India ❤ I like your video

on 0:29 you start with the lower bound of the first integration with 1/2 not 0 why?!

@shivanshnigam4015

4 ай бұрын

Because for x being 0 to 1/2 (floor(1/x))^-1 will be zero

@averageboulderer

4 ай бұрын

Because if x belongs to (1/2, 1], floor(1/x) = 1. The next interval that results in the same operator being 2 is (1/3, 1/2] and so on until (countable or discrete) infinity. Hope that gives you clarity.

@naveen.v4734

3 ай бұрын

actually he goes till that , its just that he has started with 1/2 to 1 then 1/3 to 1/2 soo eventually it will reach 0 and be included (which we will take care of in the summation)

Hello! What is the convolution of two cauchy distribution?

@drpeyam

Жыл бұрын

No idea

@kendeorosz4811

Жыл бұрын

@@drpeyam I tought you could help me.

@mwesigwadaudi5718

8 ай бұрын

​@@drpeyam😂😂😂your lying

1/2

@drpeyam

Жыл бұрын

Nope

What.

Never seen someone so excited to see pi^2/6 as an answer. P.S. where could i find the solution to getting pi^2/6

@raonimesquitadossantos7175

Жыл бұрын

The videoxof 3blue1brown about it is nice

@BridgeBum

Жыл бұрын

Google "Basel Problem"

@devd_rx

Жыл бұрын

fourier series

@erinsgeography3619

Жыл бұрын

​@@BridgeBum holy hölle!

@amineb9933

Жыл бұрын

Fourier series

When you talk about π²/6, you showed a picture of π/6! Maybe...that was actually π²/6? Please tell me!

@drpeyam

Жыл бұрын

😂😂

your thumbnail shows nearest integer, not floor

@drpeyam

Жыл бұрын

No that’s the notation for floor

@ErhardNeher

Жыл бұрын

@@drpeyam no its not, you put in brackets

I see

I don't understand this at all. I thought the answer would just be 1/2??

@sanjayg1728

Жыл бұрын

The answer 1/2 is true if the expression in the brackets was just 1/x. But it isn't. Look carefully, 1/x isn't surrounded by square brackets (although it looks like one). It is actually a floor function applied on 1/x. Just google the symbol for floor function and you'll understand.

@felixbrandt6419

Жыл бұрын

@@sanjayg1728 Thanks, man.

@NKY5223

Жыл бұрын

​@@sanjayg1728it's square brackets in the thumbnail lmao

@sanjayg1728

Жыл бұрын

@@NKY5223 Yeah, that's right.

@raonimesquitadossantos7175

Жыл бұрын

​@@sanjayg1728No, it is brackets because it's the round not the floor function.

If we substitute p = 1/x ==> dx = - p^-2 dp Also If x = 0, then p range = infinity and x = 1 then p range = 1 Now we integrate (- p^-3) dp within the p range infinity and 1 Is it workable ? and once evaluated I get the result 1/2 + C !

@drpeyam

Жыл бұрын

No that doesn’t work

@manny4148

Жыл бұрын

@@drpeyamtrue may that be, simply stating the falsehood of a solution without providing correction or guidance is both disheartening to someone who was excited about a problem you posed, as well as being unhelpful in any potential aspiration for improvement.

@kappascopezz5122

Жыл бұрын

Okay but why do a substitution like that? If you interpret the task like you just did, you can just use the power rule (x^-1)^-1 = x^(-1 * -1) = x, and then the integral becomes int_0^1 x dx which is 1/2 x² from the bounds 0 to 1, so 1/2. But all of this isn't reading the problem correctly: There is a floor function around the 1/x, which doesn't let you do any operations like this. (floor 1/x is not the same as 1/floor x)

@drpeyam

Жыл бұрын

@manny4148 Ok

@martinrosol7719

Жыл бұрын

​@@drpeyam why does your head look like a strawberry?

Answer:1/2

@drpeyam

Жыл бұрын

No

@thegrandmuftiofwakanda

Жыл бұрын

@@drpeyam Well per the problem presented on the thumbnail, yes. On the whiteboard however, you're right, no.

@wakeupthewublins69

7 ай бұрын

@@thegrandmuftiofwakandathe thumbnail is dependent on the country

@thegrandmuftiofwakanda

7 ай бұрын

@@wakeupthewublins69 I can only comment on what I can see, and what I can see is ambiguity.

Can't that be a beta function😅😂

PROF why do U write the N capital ? Thanks)

@drpeyam

Жыл бұрын

My n are illegible

@mwesigwadaudi5718

8 ай бұрын

​@@drpeyam😂😂😂😂eh

Its just x^2/2 and integral of that is 1/2

@drpeyam

Жыл бұрын

Nope

Isn't it 0.5 bro?

cool

i! ???

🙏🌺🙏

Isn’t the answer 1/2

@minecraftxd4996

Жыл бұрын

No because this is the floor(1/x)^(-1) not (1/x)^(-1)

@mokshamahey

Жыл бұрын

@@minecraftxd4996 you just said the same function

@minecraftxd4996

Жыл бұрын

@@mokshamahey how is floor(1/x)^(-1) equivalent to (1/x)^(-1)?

@newwaveinfantry8362

Жыл бұрын

@@mokshamahey Keyword: floor.

Why isnt (x^-1)^-1 just x?

@andreyfom-zv3gp

Жыл бұрын

Because this square brackets means floor function. The Floor function returns the smallest integer not greater than the argument. This aspect makes the question harder and, of course, more interesting.

aint no way bro used an integral to find a triangle

@drpeyam

Жыл бұрын

It’s not x

@jameeztherandomguy5418

Жыл бұрын

@@drpeyam bro got the supreme clickbait. Are you trying to get pepole to say its 1/2 because you didnt show the floor function on your thumbnail???

@drpeyam

Жыл бұрын

I showed the floor function in the thumbnail

@jameeztherandomguy5418

Жыл бұрын

@@drpeyam brackets can mean anything. That is not commonly accepted notation -- especially since you showed it correctly in the video sems like clickbait

@jhg8464

Жыл бұрын

@@drpeyam brackets are not floor, floor notation misses the top part of bracktes

As a first year calc student, (1/x)^-1 is literally just x. What are you even doing? 😂

@minecraftxd4996

Жыл бұрын

This isn't (1/x)^-1, this is floor(1/x)^(-1). They are two completely different functions.

@deepaparakkal4241

Жыл бұрын

@@minecraftxd4996 Woah, I didn't even realise that's the floor function. Damn.

🫣👻

Thumbnail is wrong

@drpeyam

Жыл бұрын

?

@tomasbeltran04050

Жыл бұрын

@@drpeyam The thumbnail doesn't show a floor function, just normal square brackets

@drpeyam

Жыл бұрын

That is the notation for floor…

@Kalumbatsch

Жыл бұрын

@@tomasbeltran04050 The square brackets are another common notation for the floor function, introduced by Gauss.

@budhya_

Жыл бұрын

​@@tomasbeltran04050 this notation is widely used in asian Countries and it's also called Gif (Greatest Integer Function).

no way, no hope, pi always pops up!!! :))))))

1/2

1/2

@drpeyam

Жыл бұрын

No?

@omererenylmaz413

Жыл бұрын

@@drpeyam I suppose that they misinterpreted the floor function [1/x] as parantheses (1/x). Great video!