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

  1.  @praharmitra  1. Every partial sum is, by recursion, the sum of two natural numbers, and hence must be a natural number. 2. The set of all partial sums is countably infinite.
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  2.  @praharmitra  You don't understand then. The set of natural numbers is closed under addition. All natural numbers, all the time.
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  3.  @praharmitra  Who said the limit of the series is a number? It isn't. The series tends toward infinity. In the case of pi, for example, or any convergent series, we can make the rational approximation as close to pi as we like by taking a sufficiently large number of terms. Hence the difference between series that converge and those that do not. (We never get "closer" to infinity. Or somehow end up with a negative fraction.)
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  4.  @praharmitra  You didn't say that. Math isn't supposed to be cryptic. But your comment does point up the difference between convergent and divergent series. "Two, yes, finite, yes. Infinite? No." That was all you said.
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  5.  @brian8507  "what if humans do not yet understand what a 'sum' is?" Mathematics isn't mystification, only available to initiates. Its arguments are universally true, and ultimately accessible to all who accept its axioms and rules of inference. Plato already noticed this. (The demonstration given here uses the operation of "supersum," an extension of ordinary summation. As for ordinary summation, very young children have a basic understanding.)
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  6.  @praharmitra  There are no "infinite sums," actually.
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  7. @LeNoLi.  It was infuriatingly misleading, and encouraged the notion that mathematics is the province of a Secret Society of Geniuses, rather than the study of universal truths. (For a great antidote, see the book Love and Math, Frenkel.)
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  8. That Numberphile video was nothing short of vicious. I literally hate them for doing that.
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  9.  @brian8507  🤣🤣🤣 Is it a full moon?
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  10.  @brian8507  You said: "what if humans do not yet understand what a "sum" is?" But they do grasp the zeta function. N'importe quoi. Seriously though, the concept of axiomatic systems has been thoroughly explored. You can't invoke the usual axioms of the algebra of the real numbers and get finite sums for divergent infinite series. It is really stupid to get in a pissing match about math, in order to brag to strangers that you're a mathematician, and thus privy to the Grand Mysteries (of Eleusis?) It is impossible that you do not know about what I just said.
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  11.  @dominicm1213  True, they finally did, but the original video they posted was a disgrace. Their insinuation that mathematics is some esoteric knowledge rather than the universal deductive science that it is, ultimately accessible to all (see, e.g., Plato's Meno), was the most disgraceful part of an all-around disgraceful performance.
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  12.  Gerald Mirakel  They did not say that. Therefore, in logic and mathematics, their "demonstration" is WRONG. Indeed, in logic and mathematics, equivocation is always wrong -- and deliberate equivocation is worse than wrong. Also, they did use the fact that the series S has countably infinitely many elements in order to get their result, so your comment that in physics there is no infinity is cryptic as well. Math is a universal language. Math isn't a secret society.
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  13. Bertrand Russell: "Anything can be deduced from a contradiction." A voice from the back of the room: "Zero equals one. Therefore, you are the Pope." BR: "All right. 0 = 1. Hence, 1 = 2. The Pope and I are two. Therefore, the Pope and I are one."
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  14.  @Viktor5644  No. They have to explain that they are not using the ordinary operation of addition. Whether or not pure mathematics is "consistent" with theoretical physics is very lovely, but entirely beside the point. Consistency with theoretical physics is not a means of proving mathematical theorems or justifying operations in pure mathematics. And you know it. Physics can give insights about what to try -- what mathematical theorems might be demonstrable -- and it certainly does for the gifted mathematicians (many of whom have amazing spatial intuition, and just "see" this stuff before they prove it), but physics in no way can prove those theorems.
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  15. OMG, heard about this from a more recent video. Had a super obscure prof for differential equations, was verging on getting a C in it, and infinite series solutions saved me. I was the best in the class for those. To me, this is the easy part. Never got a limit problem wrong, ever. (But I remember the one I almost got wrong, fixed it at the last minute.) This is actually because I'm not gifted in math at all. I have super high discursive intelligence, and poor spatial intuition to the point where my brain isn't quite normal. I still can't talk about it in real life, really painful. Kept me from becoming a chemist. ;(
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  16. @oooBASTIooo  Wrong, lol. It's not assumed, it follows necessarily from the axioms of arithmetic.
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  17.  @jbird-l3u  So, then it is not the usual sum, but a distinct operation. “When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’
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  18.  @marshallsweatherhiking1820  thank uou
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  19.  @graemehook3667  You can't put in a digit "after" Infinitely many digits. That fails to specify its place in the string.
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  20.  @morgjones13  I love art, yes. Logic isn't boring. Not since Cantor.
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  21.  @brian8507  Oh, I already engaged with you, for no fun nor profit. Oops.
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  22.  @paulwatson746  Just the opposite.
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  23. @bearsaremonkeys  The anger was in the fact that he didn't use logic but appeal to authority. That's for religion or politics, not mathematics. If that escapes you, read Frenkel's book for a mathematically knowledgeable lay audience. Mathematics is universal, not authoritarian.
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  24. If 1 + 2 + 3 + 4 + . . . + n + (n+1) + . . . = (--1/12), then could you just add 1 to each sIde and get 11/12? JUST KIDDING. Or better yet, add (1/12) to both sides and get zero. Yeah, that makes sense.
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  25. You did this in grammar school when you divided 1 by 3 and got 0.3333 . . . and so on to infinity. This means 3/10 + 3/100 + 3/1000 + 3/10,000 + . . . + 3/10^n + 3/10^(n +1) . . . for all N
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  26.  @KucheKlizma  "Man is mortal." We can consider this universal truth in philosophy, biology, physics, cosmology, etc., many domains besides "church." You're confusing universal with absolute. A truth can be universal and relative.
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  27. 5:52 End of story.
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  28.  @lanchanoinguyen2914  Mathematics after Cantor and modern measure theory took care of all that, but it did take well over 2000 years.
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  29. @mrigankamaulichakraborty7088  Correct, it is divergent. That was why I said the set of partial sums; and in this case, every member of the set of partial sums is also a natural number.
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  30.  @mrigankamaulichakraborty7088  Just read further in the thread.
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  31. @jfecanin310  So then what I've stated is correct. Blocked for wasting my time.
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  32. @bradmclean4988  Convergent infinite sequences yield numbers, and you generated them as a child. Dividing 1 by three generates an infinite sequence: 3/10 + 3/100 + 3/1000 + • • • + 3/10^n + 3/10^(n +1) + • • •; so does pi. But if you mean that the set of all natural numbers, under the ordinary operation of addition, cannot possibly yield another natural number, that is absolutely right. Infinity is not a number, it is a description of certain sets.
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  33. Perfect. Yes, you are the best.
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  34. Or is it half a cat? Or, is it a cat whose glass is half full? I mean half empty.
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  35.  @jeepien  Sorry! You SO beat me to it! LOL
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  36.  @moondust2365  Look at it this way, then: 1/11 = 0.090909 . . . 10/11 = 0.909090 . . . 1/11 + 10/11 = 0.9999 . . . = ((1 + 10)/11) = 11/11 = 1.
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  37.  @charlesriley2717  Zeno's paradoxes are actually highly sophisticated, and were only solved in the 20th century. The brief "resolutions," such as the observation that certain infinite series have finite sums, that you commonly see was not lost on the Greeks. The deeper solution has to do with measure theory.
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  38. No. They deliberately misled.
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  39.  @morgjones13  Numberphile is an elitist and a big, fat liar. Mathematical truths are universals. They are accessible to all, not just special initiates.
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  40.  @jamirimaj6880  I hate them.
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  41. Perfect word for it.
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  42.  @protonx80  Why fewer? ( --1/12 ) is less than zero, not fewer than zero.
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  43.  @protonx80  Well, mathematics is humanity's universal language. When explained correctly, everyone will come to agreement on it -- meaning that yes, if we agree to adopt these starting points, and agree as well to these rules of inference, then we will agree on the answer. So, you don't get your own mathematics and your own mathematical truths, no matter how strongly you may feel. Math, like every language for that matter, is a collective product. You may be used to dictating elsewhere, but you don't have that privilege here.
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  44.  @protonx80  Mathematics are not based on points of view. Neither popularity, nor voting, nor coolness, nor mightiness, nor likeability, nor likes and tweets have one iota of influence in determining mathematical truths. No form of might makes right. Mathematics is not a subset of advertising and public relations. This is what's important. Numberphile did not express a "point of view." It sought to mislead people about how mathematics works, and did so deliberately. It basically made fools of its viewers. If you think we should nevertheless be kind to them, maybe you're right. I thought this video was perfect, given what Numberphile tried to do.
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  45.  @protonx80  Of course mathematics is only one small part of the world. I think a person who would dupe others deliberately about mathematics is the arrogant one -- very deeply arrogant and elitist, because he is trying to make others believe he is superior to them. Do you know how many people saw that video and felt despair, thinking they could never learn mathematics, that they simply could never be "smart" enough? Which is, of course, nonsense. I'm glad he got his comeuppance, and that it was humorously done.
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  46.  @protonx80  Mathematics deals in theorems. If you mean hypothesis as in science, that is an empirical question. Mathematics does not rely on empirical truths in its proofs, and can't, since its theorems are about infinite sets. These videos do not deal in conjectures that have not yet been proven. The proofs are all known. Some present the theorems honestly, others take delight in tricking you. I know what I support.
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  47.  @protonx80  In short, it is not because of math that Numberphile bothers me, but because of people. People who insinuate that there is no such thing as a common truth accessible to everyone, which we can all discover, and who play games to make other people feel stupid, deserve to have their smug little butts put right in their place.
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  48.  @douggwyn9656  The objections are based on the fact that the video is wrong. Or, it's political mathematics: whatever gets the most clicks and retweets is right, and you had better agree.
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  49. Just watched this again. Loved it.
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  50.  @Viktor5644  "They did say that?" I mean, that's precise! It doesn't really respond to my comment in the first place. "In physics there is no infinity." That was your comment. Well, mathematical proofs are not empirical but deductive, precisely because they ARE about infinite sets. So, even 10^(10^100) examples, even if you had the computing power to find them, don't help you prove that something is true. They just clue you in on what you could try to prove. (See, e.g., Goldbach's conjecture).
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