# Showing the integers has the same cardinality to the Natural numbers

I would like just to check if my function which sends the positive integers numbers to the odd natural numbers and the non positive integers numbers to the even natural numbers is a bijection, more explicitly: $f:\mathbb Z\to \mathbb N, x\mapsto 2x-1$, if $x\gt0$ and $x\mapsto -2x$, if $x\le0$

I'm almost sure I'm right, it's just to be sure.

Thanks

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It's correct. You need to prove it is bijective, though. –  egreg May 14 '14 at 22:52
@egreg thanks for helping me :) –  user75086 May 14 '14 at 22:58