Bijection between Natural numbers and integers

[harv93]

My question is : Describe a bijection between the set of positive integers N and the set of integers Z.

So positive integers N - natural numbers are just 1,2,3,4,5,6,.....
and the set of integers Z is just integers, so we have -2,-1,0,1,2,3.....

There are infinite natural numbers and integers therefore i simply just have a bijection of 1 to 1 throughtout? ie set x(1,2,3) set y(-1,-2,-3) , 1 to -1 2 to -2 , 3 to-3

I think i am on the right lines , or am I?

 

[Ishuda]

My question is : Describe a bijection between the set of positive integers N and the set of integers Z.

So positive integers N - natural numbers are just 1,2,3,4,5,6,.....
and the set of integers Z is just integers, so we have -2,-1,0,1,2,3.....

There are infinite natural numbers and integers therefore i simply just have a bijection of 1 to 1 throughtout? ie set x(1,2,3) set y(-1,-2,-3) , 1 to -1 2 to -2 , 3 to-3

I think i am on the right lines , or am I?

Yes, but you have to do it for all positive integers with all integers.

Hint: If you were to divide the set of positive integers 'in half' you would have two distinct sets of positive integers each of which had the 'same number of elements'.