# Thread: Proof: infinite set minus a fintie set is infinite

1. ## Proof: infinite set minus a fintie set is infinite

Suppose B is infinite and A is a finite subset of B. Then B - A is infinite.

I am supposed to prove this...

2. Originally Posted by jzellt
Suppose B is infinite and A is a finite subset of B. Then B - A is infinite.

I am supposed to prove this...

Greetings jzellt.

The definition of the difference of B and A (B - A) could be written as:
$B - A = \{x \, | \; x \; {\epsilon} {B} \; and \; x \, {\not \epsilon} \; A\}$

Hopefully this will help make it more apparent why B - A is infinite.