- #1

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**1. If X is an infinite set and x is in X, show that X ~ X \ {x}**

**A~B if there exists a one-to-one function from A onto B.**

**Attempt at a solution**

I'm pretty much completely stumped on this problem. I know that since X is infinite then it contains a sequence of distinct points. So x in X maps onto x

_{1}of X\{x} and x

_{n}maps onto x

_{n+1}of X\{x}. Is this enough to show that is 1-1 and onto?