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## Homework Statement

Let ##f## be a continuous map from ##[0,1]## to ##[0,1].## Show that there exists ##x## with ##f(x)=x.##

**2. The attempt at a solution**

I have ##f## being a continuous map from ##[0,1]## to ##[0,1]## thus ##f: [0,1]\to [0,1]##. Then I know from the intermediate value theorem there exists an ##x## with ##f(x)=x## but I don't know how to formally prove it?