Possible title: How to Construct a Surjection Map from N to Z

[missavvy]

Surjection from N --> Z

Homework Statement

Find a surjection map,
f: N -> Z

Homework Equations

The Attempt at a Solution

I think this is equivalent to finding an injection map:
g: Z -> N

So I defined it:

g(z) =

-z, if z is negative
z, if z is positive

Is this incorrect?

 

[ystael]

1. It's not -- exactly -- equivalent to finding an injection [tex]g: \mathbb{Z} \to \mathbb{N}[/tex], because the inverse of such a [tex]g[/tex] is only a partial function [tex]\mathbb{N} \to \mathbb{Z}[/tex]; you have to extend it to be defined on [tex]\mathbb{N} \setminus g(\mathbb{Z})[/tex]. However, the result of that process is indeed a surjection [tex]\mathbb{N} \to \mathbb{Z}[/tex].

2. The function you give is not an injection; [tex]g(-1) = g(1) = 1[/tex].

It's probably easier to attack this problem by constructing the surjection you want "by hand". There are several simple algorithms which will work.