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## Homework Statement

A continuous function g: Q x Q --> R such that g(0,0)=0 and g(1,1)=1, but there does not exist any x,y\in Q such that g(x,y)=1/2

## Homework Equations

Mean value theorem?

## The Attempt at a Solution

I want to say no, because I'm sure there's something going on because the domain is not R x R....but I can't put my finger on it. Any advice?