I know the history of how set theory came about and how Cantor showed the real numbers between (0,1) were non-denumerable.(adsbygoogle = window.adsbygoogle || []).push({});

He did this by showing that they cant be put into a one-one correspondence with N (1, 2, 3...)

...So what does that really tell me? I know it tells me that the infinity of the reals is larger, but how does that tell me that N is countable itself?

Did we just assume N is countable by putting a one-to-one correspondence from N to N itself?

Why say "A set is countable if it can be put into a one-to-one correspondence with N."

Why pick N for the role of determining the denumerability of other sets?

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# How is the set of all natural numbers, N, denumerable?

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