Logic and Set Theory/Functions
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Definition, first examples
That is, a function is something where you can put in any element and you get a uniquely defined element .
- Suppose that are sets and and are functions. Suppose further that is injective. Prove that is injective.
- Prove that if is any set, then the identity on is injective.
- Conclude that if and are two functions such that , then is injective.
- Do an analogous discussion for surjectivity.
- Prove that if and are two functions such that and , then is bijective.