1
$\begingroup$

Possible Duplicate:
Uncountable minus countable set is uncountable

Proposition:

Suppose A is a countable subset of an uncountable set B. Show that B - A is uncountable.

Please help.

  • 2
    Hint: Prove that the union of two countable sets is countable.2012-12-14

1 Answers 1

3

Suppose that $B-A$ is countable. Now we find that the union of $B-A$ and $A$ which is $B$ is countable (contradiction)