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 $$g: \mathbb{Z} \to \mathbb{N}$$, because the inverse of such a $$g$$ is only a partial function $$\mathbb{N} \to \mathbb{Z}$$; you have to extend it to be defined on $$\mathbb{N} \setminus g(\mathbb{Z})$$. However, the result of that process is indeed a surjection $$\mathbb{N} \to \mathbb{Z}$$.

2. The function you give is not an injection; $$g(-1) = g(1) = 1$$.

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