# Proof: infinite set minus a fintie set is infinite

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• Feb 24th 2009, 10:25 PM
jzellt
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...

Any advice?
• Feb 24th 2009, 10:54 PM
sritter27
Quote:

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...

Any advice?

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.