- #1

math25

- 25

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Can someone please help me with this problem.

Prove that if X is countable and a is in X then X \{a} is countable.

this is what I have so far, and I am not sure if its correct:

Every non-empty set of natural numbers has a least number. Since X is not a finite set, X must be an infinite set and thus X is nonempty in N. Suppose a in X is the least element. Now consider X\{a} Since X is infinite, X\{a} is an infinite subset of N. Then there is a least element a2 in X\{a}...

thanks