Show that the set of all nonnegative integers is countable by exhibiting a one-to-one correspondence between Z + and Z manex .

To prove:

The set of all nonnegative integers is countable by showing a one-to-one correspondence between Z+​and Znonneg

Given information:

f:Znonneg→Z+

Concept used:

A function is said to be one-to-one function if distinct elements in domain must be mapped with distinct elements in codomain.

A function is onto function if each element in codomain is mapped with at least one element in domain.

Proof:

Let f:Znonneg→Z+ as

f(x)=x+1

To show: f is one-to-one.

f(x)=f(y)⇒x+1=y+1⇒x=y

Therefore, f is one-to-one.

To show: f is onto