Hm, I'm not so sure that just because the definition of a bijection is technical that it is not intuitive.
I'll start an enumeration of the rationals
1 1/3
2 1/4
3 1/5
...
If you can prove that you can do this, is that really so non-colloquial? It is certainly what we mean by "as many" for all finite sets, so what is wrong with doing this for infinitely many sets?
I'll start an enumeration of the rationals
1 1/3
2 1/4
3 1/5
...
If you can prove that you can do this, is that really so non-colloquial? It is certainly what we mean by "as many" for all finite sets, so what is wrong with doing this for infinitely many sets?