Math 2.0

definition

Function

Definition

Let AA and BB be sets. A function from AA to BB is a binary relation f⊆A×Bf \subseteq A \times B such that, for each a∈Aa \in A, there is exactly one b∈Bb \in B with (a,b)∈f(a, b) \in f. This bb is the value of ff at aa, written f(a)f(a). The notation f ⁣:A→Bf \colon A \to B says that ff is a function from AA to BB.

Remarks

The set AA is the domain and the set BB is the codomain of ff. Many authors take the triple (A,B,f)(A, B, f) as the function. Then two functions with the same pairs but different codomains are different. Two functions f,g ⁣:A→Bf, g \colon A \to B are equal when f(a)=g(a)f(a) = g(a) for each a∈Aa \in A. Other names are map and mapping.

Explanations

L1 human

A function is a machine: you put in an element aa of AA, and it gives back one element f(a)f(a) of BB. Each input gives exactly one output, but two inputs can give the same output. For example, f(x)=x2f(x) = x^2 on R\mathbb{R} sends both 22 and −2-2 to 44.

What this node needs for W2
  • edge instance_of in: one example (0 of 1)
  • edge not_instance_of in: one non-example that fails one clause (0 of 1)

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347 nodes use this node, directly or through other nodes.

Sources

  1. Web https://en.wikipedia.org/wiki/Function_(mathematics), lead section

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