- #1
cchatham
- 5
- 0
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 x1 of X\{x} and xn maps onto xn+1 of X\{x}. Is this enough to show that is 1-1 and onto?
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 x1 of X\{x} and xn maps onto xn+1 of X\{x}. Is this enough to show that is 1-1 and onto?