Search problems

1 problem matches “supremum”. Clear

Visitors search a sample. Sign in for free to search every problem. Sign in

1. Smallest bound on function differences ●●●○○ 50 ptsThe function $f(x)$ is defined on $[0,1]$ and satisfies $f(0)=f(1)$, and for any $x, y \in [0,1]$ with $x \neq y$, we have $|f(x)-f(y)|<|x-y|$. Find the smallest real number $m$ such that for every such function $f$ and any $x, y \in [0,1]$, we have $|f(x)-f(y)|<m$. Give your answer as a decimal.