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:
$\displaystyle B - A = \{x \, | \; x \; {\epsilon} {B} \; and \; x \, {\not \epsilon} \; A\}$
Hopefully this will help make it more apparent why B - A is infinite.