Any example of contraction

1.	Any example of contraction
Answer» For example, let f : [0,1] → [0,1] by f(x) = 0 for 0 ≤ x ≤ 1/2 and f(x)=1/2 for 1/2 < x ≤ 1. Then f(f(x)) = 0 for all x, so f2 is a CONTRACTION but f is discontinuous. It was important in the PROOF of the contraction MAPPING theorem that the contraction constant c be strictly less than 1.

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