Intermediate Value Theorem/Historical Note

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Historical Note on Intermediate Value Theorem

This result rigorously proves the intuitive truth that:

if a continuous real function defined on an interval is sometimes positive and sometimes negative, then it must have the value $0$ at some point.

Bernhard Bolzano was the first to provide this proof in $1817$, but because of incomplete understanding of the nature of the real numbers it was not completely satisfactory.

Hence many sources refer to this as Bolzano's Theorem.

The first completely successful proof was provided by Karl Weierstrass, hence its soubriquet the Weierstrass Intermediate Value Theorem.