/sci/ - Science & Math

>>12454519
>>12454540
>Sets A_i, element j of A_i is a_ij. Define a map by f(a_ij)=(2^i)*(3^j).
If you read "countable" in the "enumerable" direction A->N, with powers of 2 and 3 (an answer exactly like this is also on the SE thread of the topic) instead of N->A, it might even get a tad more difficult than in the other direction. I think, not sure, that with A in the domain, it might raise questions like whether the procedure being given a [math]a_{ij}[/math] in the union of all [math]A_i[/math]'s automatically means we know which [math]A_i[/math] that [math]a_{ij}[/math] is from.
In any case, almost everybody will take their functions apriori be packed with so much information that the choice involved in the N->A proof goes through.

That said, here's a nice rant against is

http://math.fau.edu/Richman/docs/venice.pdf