Comments by "Lawrence D’Oliveiro" (@lawrencedoliveiro9104) on "Numberphile" channel.

  1. 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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  2. I don’t know why. His theorems are so straightforward. It’s like basic knowledge that every programmer should have absorbed into their DNA.
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  3. 1:55 If the board wrapped around, then that open tour would become a closed tour.
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  4. 7:03 Is the natural language of growth only in the real numbers. Once you go into the complex plane, you see that it is the natural language of trigonometry as well. Where you have periodic functions, rather than infinitely growing ones. And Euler’s famous identity.
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  5. Maybe it should have been called “Tralfamadorean” arithmetic. The Moon is not that far from the Earth, after all.
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  6. 15:48 Don’t we all, JHC, don’t we all ...
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  7. 10:37 But can you in fact formally prove that you can “keep on playing the same game”?
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  8. 7:17 In other words, if you pulled apart the bits and randomly stuck them back together, you only have a 1 in 12 chance that the result can be solved.
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  9. 0:47 See, I was taught that the “natural” numbers ℕ did not include zero, while the “whole” numbers 𝕎 did.
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