# Intermediate value theorem/Bisection method/3/Method

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Let
be
real numbers,
and let
denote a
continuous function
such that
and .
Then the function has a zero within the interval, due to
the Intermediate value theorem.
Such a zero can be found by the *bisection method*, as described in the proof
of the Intermediate value theorem.
We put
and ,
and the other interval bounds are inductively defined in such a way that
and
hold. Define
and compute . If
,
then we set

and if , then we set

In both cases, the new interval has half the length of the preceding interval and so we have bisected intervals. The real number defined by these nested intervals is a zero of the function.