- #1
JT73
- 49
- 0
I know the history of how set theory came about and how Cantor showed the real numbers between (0,1) were non-denumerable.
He did this by showing that they can't 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?
He did this by showing that they can't 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?