Comments by "zenith parsec" (@zenithparsec) on "How to Count" video.

30:00 Counting is only well-defined if you accept that everything is frozen at the beginning. (in JavaScript, for example, you could change the length of the array (ordered set) in the comparison function, which leads to all kinds of bad things happening when it keeps on using the old length in some parts with the new length in others) Mathematics generally assumes you're not being evil.
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16:24 But why would you cover the extensionality definition up? Unrelated: sets A and B appear to have the same members in a different order. And that sets are unordered. i.e. they are the same set so they contain the same number of elements by extensionality. What if A or B contained numbers? [ 16:15 "The easiest way to do that is...." no. The easiest way is " { { {a}, b } , { {b}, a } , { {c}, c } }" ] [ brackets ] { braces } ( parentheses ) <angle brackets> (-8, 80, 8) <= how many emoticons are there in the ordered set? And how many are inside it? ;] 17:30 : Rhetorical question: Is (2,5) distinct from (5,2) in all systems? What about ones which are defined only by the magnitude of their position vector? The metric system is important, but what about the system of metrics? [ Mahalanobis and Euclid walk into a bar, ...] 18:00 Ordered pairs are being defined with a very handwavy feel. How do you make sure each member has a unique "number" associated with it again? Doesn't that require some method of matching elements between sets, the problem you are trying to solve?
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35:04 Next, prove induction works, without using induction (because that's what you're trying to prove.) I'll wait. 36:08 You are assuming what you are trying to prove: that 1/2 of every even number is a unique number. What if they aren't unique once you get up over 100 billion billion digits? [Still waiting for the induction proof.]
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@angelmendez-rivera351 He used induction. You can't prove induction except by induction, which was the joke. I'm sorry you didn't understand.
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