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Solution Proposal Functional Programming Sheet 7 Proof: Let S be an arbitrary chain of D1, let f : D1 D2 and g : D2 D3 be
 

Summary: Solution Proposal Functional Programming ­ Sheet 7
Exercise 1
Proof: Let S be an arbitrary chain of D1, let f : D1 D2 and g : D2 D3 be
continuous functions. We then have:
(g f)(S) by definition of composition
= g(f(S)) f is continuous
= g(f(S)) g is continuous
= g(f(S)) by definition of composition
= (g f)(S)
Therefore, also the composition (g f) : D1 D3 is continuous.
Exercise 2
(a) Claim: For g1, g2 Z Z , we have:
g1 ZZ
g2 sum(g1) ZZ
sum(g2)
Proof: Let g1, g2 Z Z with g1 ZZ
g2. By definition of ZZ
,
one can show sum(g1) ZZ
sum(g2) by showing that

  

Source: Ábrahám, Erika - Fachgruppe Informatik, Rheinisch Westfälische Technische Hochschule Aachen (RWTH)

 

Collections: Computer Technologies and Information Sciences