# Help with a Proof

• Nov 18th 2008, 08:01 PM
mattman3377
Help with a Proof
The set of all integers (positive , Negative, and 0 ) is denumerable?

How do you prove this? I have

Set Z = (....-3, -2, -1, 0 , 1 , 2 , 3 ....)

Proof : Z = ( 0, 1, -1, 2, -2, 3, -3...) is this right??

Thank you so much!
• Nov 18th 2008, 08:12 PM
TheEmptySet
Quote:

Originally Posted by mattman3377
The set of all integers (positive , Negative, and 0 ) is denumerable?

How do you prove this? I have

Set Z = (....-3, -2, -1, 0 , 1 , 2 , 3 ....)

Proof : Z = ( 0, 1, -1, 2, -2, 3, -3...) is this right??

Thank you so much!

Not quite you need to define a bijection (1-1 and onto) function from
$\mathbb{Z} \to \mathbb{N}$

Hint: use a piecewise and send the non positive integers (0,-1,-2,...) to the odd natural numbers and send the positive integers to the even natural numbers.

Good luck
• Nov 18th 2008, 08:14 PM
mattman3377
First, Thank you so much for your speedy response!

I have a test tomorrow and this is all the teacher gave us to study for ( what I wrote to you)

I'm not quite sure what a bijection means?
• Nov 18th 2008, 08:18 PM
TheEmptySet
Quote:

Originally Posted by mattman3377
First, Thank you so much for your speedy response!

I have a test tomorrow and this is all the teacher gave us to study for ( what I wrote to you)

I'm not quite sure what a bijection means?

bijection is a function that is both 1-1 and onto