Competitions

Putnam proofs — Proofs

Putnam-level statements to prove in full. Name every theorem you use and check its hypotheses — that is what the graders reward.

Problem 1 of 21
Analysis

Prove that every continuous function f ⁣:[0,1]→[0,1]f\colon[0,1]\to[0,1] has a fixed point, i.e. some cc with f(c)=cf(c)=c.

Write a full proof on paper. There is no answer box — when you are ready, reveal the solution and compare your argument.

Proof practice — Putnam course