10: Functions
- Page ID
- 83450
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- 10.1: Basics
- Function(working definition): a rule which assigns to each input element from a set A a single output element from a set B
- 10.2: Properties of Functions
- Surjective Function: a function whose image is all of its codomain — that is, every element of the codomain is an output for the function;
- 10.3: Important Examples
- identity function (on a set A ): the function A→A defined by a↦a
- 10.4: Composition of functions
- Composite Function: a function A→C created from given functions f:A→B and g:B→C by a↦g(f(a))
- 10.5: Inverses
- Suppose f:A→B is a function. By definition, f associates an element of B to each element of A. Sometimes we want to reverse this process: given an element b∈B, can we determine an element a∈A such that f(a)=b?