# proof of countable

• May 1st 2008, 11:23 AM
natewalker205
proof of countable
Prove that the set {1,2,3}xnatural numbers is countable.
• May 1st 2008, 11:30 AM
Isomorphism
Quote:

Originally Posted by natewalker205
Prove that the set {1,2,3}xnatural numbers is countable.

Hint:
if $X = \{1,2,3\} \times \mathbb{N}, \text{consider } f:X \to \mathbb{N}$ defined as $f((i,n)) = 3(n-1)+i$

P.S: Though I have tailored this definition for this problem, any cartesian product of countable sets is countable