Пікірлер

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  @ariyaebrahimi8778 күн бұрын

  Really fantastic! The only thing I couldn't understand was the problem with the nature of Dedekind cuts. Is it a model or is it the "definition" of the system of real numbers? I mean aren't there concrete definitions so we can check them mechanically? why leaving it to philosophy?

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  @dodecahedra5 күн бұрын

  I talk about this a bit in the beginning. Yes, you can consider Dedekind cuts a model. Then, since we can show that the cuts satisfy all the axioms of the real numbers, something out there exists that acts exactly like the real numbers should act. So that's good enough for most. Or you could make the stronger claim that this is what the real numbers REALLY ARE.

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  @thomasj810513 күн бұрын

  If your students can't handle it...

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  @itsthecorcaigherman15 күн бұрын

  Great video. How do we know that each vertex configuration defines a unique solid?

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  @octaviosegui728517 күн бұрын

  jaa love u! greetings from Argentina

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  @climitod852428 күн бұрын

  9:10 what a cool ass explanation I've never heard a professor explain velocity like this. I see your analysis courses are taught at a highschool is this actually analysis or just ap calc?

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  @dodecahedra28 күн бұрын

  It's pretty much just AP Calc, but going into more detail on some things, including all the proofs.

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  @trishanuagarwal9220Ай бұрын

  Nice proof sir

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  @PAPLOAFАй бұрын

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  @PAPLOAFАй бұрын

  Nice😀

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  @d_15745Ай бұрын

  37:22 NO! Please explain more! I am confused on why you were able to prove ~P v Q in the subproofs. You mentioned you could not do this in the video that has problem #14 ( kzread.info/dash/bejne/q2eFlruboJnTlKw.html )

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  @Eden_LaikaАй бұрын

  Honestly? His best work since YSIV.

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  @hamseabdihakinmohamoudhuss7272Ай бұрын

  Thanks for that useful explanations❤❤

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  @superlative_custard2 ай бұрын

  Brilliant - love the four level explanation

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  @d_157452 ай бұрын

  I am currently studying logic as my independent study and your videos have drastically helped me understand propositional logic so much better! Thank you so much!

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  @pathueagle2 ай бұрын

  10 years later and Mr.Rose is still the GOAT 🐐🔥💯

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  @KT-vi7gd2 ай бұрын

  Good ! Clear explanation.

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  @pencilled_robin2 ай бұрын

  This explains it so clearly! Thank you 😊

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  @oxygen26712 ай бұрын

  In example 14 why don’t we only use the previous proof to prove it

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  @dodecahedra2 ай бұрын

  We're just... not doing that. These are exercises, so we don't use any previous results.

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  @Saif-ur-Rehman4872 ай бұрын

  university name please ?

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  @TimCooper202 ай бұрын

  If the set of all real numbers can be constructed from the rationals and you must have a corresponding A and B, then how can the cardinality of the reals be greater than the rationals? Wouldn't you need a bijection relationship from Q X Q* ( Cartesian product) to R in order for Dedekind Cuts to work?

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  @dodecahedra2 ай бұрын

  ℚ, the set of rationals is indeed countable, as is ℚ⨉ℚ the set of ordered pairs of rationals, but we're not matching each real to a rational or to an ordered pair of rationals, we're matching each real to a SET of rationals. There are an uncountable number of sets of rationals.

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  @TimCooper202 ай бұрын

  @@dodecahedra" uncountable number of sets of rationals "? is there a axiomatic proof of that somewhere? So you are saying the infinite number of sets of rationals is the same cardinality as the set of Reals? i.e the continuum?

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  @studentdastanay76442 ай бұрын

  which age group do you teach to ?

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  @dodecahedra2 ай бұрын

  High school

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  @studentdastanay76442 ай бұрын

  @@dodecahedra so age 14 to 18 ?

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  @user-wr9zu7ck2t2 ай бұрын

  Oh stranger on the internet, you might have just saved me, thank you

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  @angelam.gallo-birkley.11602 ай бұрын

  Help me

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  @angelam.gallo-birkley.11602 ай бұрын

  Hi😊

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  @daveglen45783 ай бұрын

  (20:17)...yes, you are the best! 😁Thanks for your knowledge and hard work.👍

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  @daveglen45783 ай бұрын

  Thank you very much. Your vids helped a lot😁👍

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  @jarelmontes75833 ай бұрын

  For #21, why did we shade in the areas towards the pi/2 and towards 3pi/2 ? I thought the closer we got to those points, the GREATER it becomes. But aren’t we looking for areas where it is LESS than bcuz we have the less than sign?? I was understanding everything until this point.

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  @dodecahedra3 ай бұрын

  Not sure exactly what you're talking about. Near π/2, cosine is small, approaching 0. There is a small error with this solution though. π/2, 3π/2, etc. should be excluded since secant is undefined at those values.

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  @jarelmontes75833 ай бұрын

  For #18, could we also have written, if they gave us the restriction from [0, 2pi), (0, pi/3) U (5pi/3, 2pi) ?????

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  @dodecahedra3 ай бұрын

  Yes.

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  @heyimd91383 ай бұрын

  this is soooooo much easier to understand holy shit dude.

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  @dddd-ci2zm4 ай бұрын

  Great video! This cleared up some ideas that other videos gloss over like the idea that we really have ~(~a) and the bottom Symbol for contradiction

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  @wondr0us9294 ай бұрын

  Dude you are amazing <3

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  @yopenzo4 ай бұрын

  Alas, what a pity. You are a good one, but your continued aaahhh/uuuuuhhh/oooooh in your speech is almost unbearable. And now a baby screaming. Unwatchable.

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  @yopenzo4 ай бұрын

  You are fun because catastrophic. And viceversa. 👍

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  @feraudyh5 ай бұрын

  At 5:58 I can tell that the thought police are coming to get you for teaching logic and clear-thinking!

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  @FranciscoMarzoa5 ай бұрын

  07:10 probably a stupid question, but couldn't you just get a contradiction by conjunction introduction with 1 and 14 directly?

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  @nequidnimis8885 ай бұрын

  Thank you for the detail and clarity you used to break down this proof! As someone who is trying to self-learn real analysis, this is most helpful and appreciated.

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  @FranciscoMarzoa5 ай бұрын

  32:36 lol, that was totally unexpected. 😂

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  @mariaaparicio42765 ай бұрын

  Thank you soso much, I've been searching for good natural deduction videos and this is the only good video I could find. You will probably save my resit on logic, so thank you so much!

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  @one_logic5 ай бұрын

  Why assert the existence of the empty set when you can take the union set of the subset of the infinity set that contains the empty set?

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  @codework-vb6er5 ай бұрын

  Awesome !

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  @studentdastanay76445 ай бұрын

  equation of plane containing y axis and passing through 1 2 3

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  @studentdastanay76445 ай бұрын

  .

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  @Bello777775 ай бұрын

  ❤

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  @Bello777775 ай бұрын

  You're coool.... lov3d your videos..

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  @imumbreon30525 ай бұрын

  this guy sold me fent

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  @user-nl8fv9in4h6 ай бұрын

  Continue with this teaching

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  @Harsh-se5ch6 ай бұрын

  🙇‍♂🙇‍♂🙇‍♂🙇‍♂🙇‍♂

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  @michmarch20466 ай бұрын

  Thx

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  @seanhunter1116 ай бұрын

  I love the fact that he’s explaining one of the most famously intellectually challenging things in maths and there are children screaming constantly in the background

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  @seanhunter1116 ай бұрын

  What an incredible explanation of the least upper bound. It feels completely inevitable.

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  @RyantheCanuckpirateАй бұрын

  One of the most metal math videos in existence

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  @theemptylive17396 ай бұрын

  The explanation for fitch-style existential instantiation around 27:40 was incredibly helpful, thanks!

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  @dodecahedra6 ай бұрын

  Existential ELIMINATION