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Functions

Black box that accepts object as input and produces another object as output

Definition in terms of sets

• f:R => S

  f is function from R to S
  R domain of f, S codomain of f
  R => S arity (functionality) of f

• Application f(a)

  a in R, f(a) in S

• Equality f=g

  f,g: R => S f(x) = g(x) (for all x)
  (extensionality principle)

• Composition f o g

  f:R => S, g:S => T
  f o g: R => T
  (f o g)(x) = g(f(x))