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## Homework Statement

Two functions in F(S,F) (or going from the vector space S to the vector space F) are equal if and only if they have the same value at each element of S. True or False?

## Homework Equations

How can you prove: if two functions, x and y, are equal then they have the same value at each element of S?

## The Attempt at a Solution

By the definition of equivalence, I can see that if two functions have the same value at each element of S, they are equal. However, I'm not sure how to show the converse.