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Continuous function/Closed interval to itself/Fixed point/Exercise
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Let
f
:
[
a
,
b
]
⟶
[
a
,
b
]
{\displaystyle f\colon [a,b]\longrightarrow [a,b]}
be a continuous function from the interval
[
a
,
b
]
{\displaystyle {}[a,b]}
into itself. Prove that
f
{\displaystyle {}f}
has a fixed point.
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