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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.


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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
up vote 2 down vote accepted

Yes it is.
Write up its inverse.

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Thanks for your help :) – user75086 May 14 '14 at 22:59

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