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Partial Functions

• Any result is computed in a finite number of unfoldings.

  (a,b) in graph(factorial)
  ->(a,b) in graph(fac_i) (for some i)

• Consequently

  graph(factorial) c union_i=0^oo graph(fac_i)

• Thus

  graph(factorial) = union_i=0^oo graph(fac_i)

Factorial function can be totally understood in terms of the finite subfunctions fac_i!