- #1
mpitluk
- 25
- 0
How do I explicate "A is countable"?
My attempt:
In set theory, every thing is a set, even functions. Thus when we say "A is countable in M" we mean that there is another set B in M that contains {naturals} and A as ordered pairs.
I'm having trouble spelling out the "as ordered pairs" part.
Is is: B in M that contains N and A in ordered pairs such that (a, n) where a ∈ A and n ∈ N and for every a there is exactly one corresponding n and for every n there is exactly one corresponding a?
Is there an easier way to write this?
My attempt:
In set theory, every thing is a set, even functions. Thus when we say "A is countable in M" we mean that there is another set B in M that contains {naturals} and A as ordered pairs.
I'm having trouble spelling out the "as ordered pairs" part.
Is is: B in M that contains N and A in ordered pairs such that (a, n) where a ∈ A and n ∈ N and for every a there is exactly one corresponding n and for every n there is exactly one corresponding a?
Is there an easier way to write this?