Comments by "Lawrence D’Oliveiro" (@lawrencedoliveiro9104) on "Infinity is bigger than you think - Numberphile" video.

Fractals seem like a very convincing illustration of infinity within a finite space.
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0:15 >>> import math >>> print(math.isnan(math.inf)) False Python seems to disagree with the notion that infinity is not a number.
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1:30 It’s the infinity of the counting numbers, which is probably why it’s called “countable”.
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6:18 There is a problem with that construction: it never terminates. Remember what an “algorithm” is: it’s supposed to produce an answer after a finite number of steps. Therefore, the Cantor diagonal construction is not an algorithm. So your proof that the infinity of the reals is greater than the infinity of the integers can never actually be completed.
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@MuffinsAPlenty The specification of each decimal place allows you to define convergence. That still doesn’t allow for Cantor’s diagonal proof.
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@MuffinsAPlenty But the Cauchy construction only gives you one real. At each step, you get closer to the number you are approximating. Cantor’s construction is infinite and does not converge: after any number of steps, you are no closer to the final answer than when you started.
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You could flip the proof on its head: you could say that, every time the diagonal construction produces a new number, you can always add it to the list. Or, look at it this way: it takes an infinite number of steps to produce a new number, but only one step to add it to the list. Or, to put it another way, in an infinite construction, who gets the last word?
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