Prove that if A is any countably infinite set, B is any set, and
To prove:
If A is any countably infinite set, B is any set and
Given information:
A is any countably infinite set, B is any set and
Proof:
Given:
A is a countable infinite set.
B is a set.
Let us define the function f as:
f one-to-one:
Let
However, we know that the image of a is an element y such that
Similarly, we know that the image of b is an element z such that