Letting we observe that

However, there is no such that . Why is this not a counterexample to Bolzano’s theorem?

This does not contradict Bolzano’s theorem since is not continuous on the interval since it is not defined at .

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Stumbling Robot

A Fraction of a Dot
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Explain why tan x does not violate Bolzano’s theorem

Letting we observe that

However, there is no such that . Why is this not a counterexample to Bolzano’s theorem?

This does not contradict Bolzano’s theorem since is not continuous on the interval since it is not defined at .