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Homework Statement
Let S be in finite and, A a subset of S be finite.
Prove that that the cardinality of S = the cardinality of S excluding the subset of A.
Homework Equations
The Attempt at a Solution
We can write out the finite subset A as (x1, x2, ... xn) which can be put into a one to one correspondence with N. S is infinite so a bijection to N is not possible by definition. The cardinality of S excluding A is still uncountable but I don't see why they MUST have the same cardinality.