Altering an Infinite Set does not change cardinality Let X be an infinite set. Show that adding or subtracting a single point does not change its cardinality. 
I have a plan but need help writing the actual proof. 
I need to show that it doesn't matter which point is removed, and then I can use the fact that X is in one-to-one correspondence with a proper subset to prove this. 

HINT: Given two elements $x,y\in X$ there is a permutation of $X$, $\pi$, such that $\pi(x)=y$ and $\pi(y)=x$.
