Question

Proof: if a set A is countable and there is a surjection f:A->B for some set B, then B is countable.

Answer 1

I know that if A is countable then A is either finite or A~N and a surjection is that every point in A maps onto B but how do I prove this??

Answer 2

if there is a surjection does that mean that A can't be an empty set?

Answer 3

since A is a countable set, then A~B is subjectice, so then since surjection A~B, choose a Bijection N~B impiles that B is countable

Answer 4

N~B implies B is subjective. and A is infinite

Answer 5

what does subjective mean?

Answer 6

sorry I meant surjective*

Answer 7

Oh okay and N~B implies that A is infinite?

Answer 8

yes, seems like you got it!

Answer 9

Ok, thanks!

Answer 10

Welcome, you are ready for law school

Answer 11

Uhhhhhhhhhhhhhhhhhhhhhhh.....................cool!

Answer 12

If you need any help, feel free to notify