Comments by "L.W. Paradis" (@l.w.paradis2108) on "Mathologer" channel.

  1.  @luizsouto4019  Yup. Mathematical truths aren't universal and accessible to everyone when explained properly, they depend on how cool you are. Everything is a subset of advertising, so why not mathematics?
    2
  2. @amigalemming  "Does not naturally follow?" Well, that's pellucid.
    1
  3.  @amigalemming  I have a better idea. Watch this video a couple of times.
    1
  4.  @theunholybanana4745  No, that's proved, not assumed. Just like it is proved closed under multiplication but not subtraction or division. A successor function is postulated, not closure under addition. See the Peano postulates.
    1
  5. And it's not the usual operation of addition over the real field, either.
    1
  6. You actually thought that? That if they have PhDs, maybe they're right? Mathematics is the opposite of appeal to authority. Those guys were wrong -- and they are jerks. It's real simple.
    1
  7. 13:35
    1
  8. Just the opposite. N, R, P(R), . . . are all already complete. All the numbers are already there. "Infinity of time would prevent anything from moving" makes no sense. Were you thinking of one of Zeno's paradoxes?
    1
  9. ​ @josephmathes Yes, please!!! The Continuum Hypothesis!
    1
  10. I don't know why I'm having so much trouble with this intuitively. Is this set in one-one correspondence with the power set of N, hence uncountable? At first I thought it would have to be countable, until this occurred to me. Please help!! 😊
    1
  11. My favorite mathematician.
    1
  12.  @danjbundrick  No. Do not listen to Numberphile. Really. Do not.
    1
  13. It was wrong. Desperately wrong. Worse yet, trying to make YOU feel stupid.
    1
  14.  @kacperxt371  Excellent.
    1
  15. @Hassan Akhtar Suppose each pause is one-half the length of the previous pause?
    1
  16. Sure. It's a lot like the birthday paradox in probability. We knew that.
    1
  17. I know people know, but just for the record: proof by contradiction. If rearranging the terms of a given infinite series leads to a contradiction, then rearranging the terms of that series is forbidden. Simple, but not satisfying. So, you study these series in depth and find that they either converge to a finite sum at the limit, or they do not. Etc. Everyone has known about the existence of convergent infinite series since 5th grade, if not before, perhaps without being aware of it: 1 ÷ 3 = 0.3333 . . . 0.3333 . . . = 3/10 + 3/100 + 3/1000 + 3/10,000 . . . . (Notice that wherever you stop, you have a partial sum that is less than 1/3. But the infinite decimal expansion does not have to be calculated in some sense: it already exists as complete.)
    1
  18.  @michaellombardi3638  Very nicely explained.
    1
  19.  @morgjones13  Mathematics is never "magic." It is universal. The set of all partial sums of the natural numbers under the usual definition of summation contains only natural numbers.
    1
  20.  @Dashman100  The Numberphile video is illogical. All mathematicians deal with infinity all the time. Every mathematical proof is true of some well-defined infinite set of mathematical objects.
    1
  21.  @PSOnoni  😅 thanks 😉
    1
  22.  @TheBuzzSaw  Physical theories NEVER serve as proofs of mathematical theorems. Numberphile hid false assumptions, it didn't explain why a different branch of mathematics, with different definitions for operations, has a string theory application. The application does not matter to the mathematical proof. Whether string theory is right or wrong is irrelevant.
    1
  23. You are a rock star!
    1
  24.  @kingkartabyo6206  I know. This video is great. Numberphile were obnoxious. Of course they misled people deliberately. I don't think "post truth" is very funny anymore, sorry.
    1
  25.  @KucheKlizma  See the book I recommended.
    1
  26.  @ljdellar8123  No, he didn't.
    1
  27.  @TheNadscratcher  I was using (--1/12) as a JOKE. But the point stands.
    1
  28.  @TheNadscratcher  Marks have to be from the set of natural numbers? I thought rational numbers were included. You know, like 4 1/2 on a scale of 5.
    1
  29.  @TheNadscratcher  Right. Fewer apples, less applesauce. Partitive. "Zero marks!" "[He deserves] less!" I would have said that.
    1
  30.  @protonx80  However you like. I suggest you ask someone who sat in jail for a crime they had nothing to do with, or ask someone whose child was gunned down by police because they mistakenly thought his cell phone was a weapon, whether there is such a thing as "truth," or whether it's all just opinions. (Are Innocence Projects news to anyone? Still?) Infinite series aren't about anybody's "opinion," in any sense of that word. But I see it has to be your way. No worries. Have it your way. I just wonder how you expect to force it on everyone else, when it comes to math, no less.
    1
  31.  @protonx80  Please stop. You've just made me feel sorry for you. (Look up Bertrand Russell sometime, and Pythagoras, and Plato. Libraries have books on the philosophy of mathematics. Really. It's true. And from the other side, there is no single subject that has had a more profound influence on philosophy than mathematics.)
    1
  32. Except that it . . . isn't.
    1
  33. Think about this, too -- why would an area have a negative value? Don't take it for granted. (I'm not suggesting it's wrong . . . Just to think about it. When does it make sense, when not?)
    1
  34. @Brauggi the bold Interesting, though, isn't it? Definite integrals can have negative values, but the area of any polygon is positive.
    1
  35. @Brauggi the bold I'm not suggesting there is. I'm suggesting that we too often take mathematics as though it were a set of little recipes, without thinking about what we are doing and why. I'm not into that "mystical" crap, so I do know what you mean.
    1
  36. @Brauggi the bold P. S. Not a fan of Numberphile. Takedown well deserved.
    1
  37. @Brauggi the bold I did actually study math, and metamathematics, and did a Master's thesis on Zeno's Paradoxes, which as we know are not trivial.
    1
  38. Oh yes it does.
    1
  39.  @GodzillaGoesGaga  Modern calculus does not use infinitesimals. Mathematicians saw they were contradictory in standard analysis.
    1
  40. Only on the Internet could people argue about mathematics.
    1
  41.  @stanbondarev9256  Numberphile! Never, never, never, never, NEVER listen to those jerks. Never. Really. Never.
    1
  42.  @ejrupp9555  Yeesh. Believe it or not, Aristotle got tangled up in this. The set of natural numbers, which are in one-to-one correspondence with the digits of the infinite expansion 9.999 . . . , is not being generated somewhere. It is already complete. To say it "goes on forever" is a metaphor. It isn't "going" anywhere. And it is not temporal in that sense, either, as might be thought of as implicit in the metaphor. There is no unfolding through eternity. It simply IS.
    1
  43.  @ejrupp9555  You are confusing notation with what the notation refers to. 9.9999 . . . is precisely equal to 10, just as 0.3333 . . . is precisely 1/3. 9.9999 . . . and 10 are equal, as are 0.3333 . . . and 1/3.
    1
  44.  @ejrupp9555  I already showed you how you're wrong. You're assuming 9.999 . . . "can never reach 10." It IS 10. All the digits are THERE. They are not waiting for you (or anyone) to pluck them from some netherworld and to write them down or conceive them. They are all there, just like the set of all natural numbers already IS. This is your error. I can't force you to see it.
    1
  45.  @ejrupp9555  Read Shadman Shahriar's explanation of why REPEATING DECIMALS are rational numbers. He explains it perfectly.
    1
  46.  @ejrupp9555  Infinity is neither rational nor irrational. It is not a number. It is, first of all, a property of certain sets.
    1
  47.  @ejrupp9555  There is no such real number. Between any two distinct real numbers there are infinitely many real numbers. Read the first chapter of any decent topology book, or the first few chapters of a real analysis book. You don't need abstract algebra or calculus to understand the initial description of the real number line. Your desire to speculate about it is enough. IOW, you are wrong in interesting ways.
    1
  48.  @ejrupp9555  What's the smallest positive real number? (Trick question)
    1
  49. I guess you'd have to subtract "the smallest positive real number" from 10 to get . . . Oh wait.
    1
  50.  @Chris-5318  This is why most teachers quit within five years.
    1