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This is one formulation of the intermediate value theorem. en.wikipedia.org

The intermediate value theorem establishes the second player must be satisfied the cake is halved at some point. en.wikipedia.org

It is reminiscent of the intermediate value theorem for continuous functions. en.wikipedia.org

These order-theoretic properties lead to a number of important results in real analysis, such as the monotone convergence theorem, the intermediate value theorem and the mean value theorem. en.wikipedia.org

Another characterization says that the intermediate value theorem holds for all polynomials in one variable over the (ordered) field. en.wikipedia.org

However, as with the intermediate value theorem, an alternative version survives; in constructive analysis, any "located" subset of the real line has a supremum. en.wikipedia.org

We can imagine the intermediate value theorem's failure as resulting from the ability of an infinitesimal segment to straddle a line. en.wikipedia.org

By the intermediate value theorem, "g" has a zero in "a", "b"; this zero is a fixed point. en.wikipedia.org

A proof of that fact requires the intermediate value theorem from elementary calculus. en.wikipedia.org

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