# Help with Equivalence Relations

• Apr 26th 2010, 11:03 AM
Nach1855
Help with Equivalence Relations
Here is my problem,

Let A be a set of all numbers divisible by 3. Show that A is equipotent to B. Important: When you find the bijection from A to Z (all integers) you need to prove it is a bijection.
• Apr 26th 2010, 11:59 AM
Plato
Quote:

Originally Posted by Nach1855
Let A be a set of all numbers divisible by 3. Show that A is equipotent to B. Important: When you find the bijection from A to Z (all integers) you need to prove it is a bijection.

From the given $A=\{3j:j\in \mathbb{Z}\}~~$. Define $\Phi:A\to \mathbb{Z}$ by $3j\mapsto j$.