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Functions as Sets

Every function f:R => S can be represented by its graph:

graph(f)	= { (x,f(x)) | x in R }
	c R ×S

Successor function on Z
{ ..., (-2,-1), (-1,0), (0,1), (1,2), ...}

• Function application

  f(a) = b <=> (a,b) in graph(f)
  f(a) := apply(graph(f), a)

• Function composition

  graph(f o g) =
  { (x,z) |

  x in R and, for some y in S,

  (x,y) in graph(f) and

  (y,z) in graph(g)}