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Bolzano's Theorem
Bolzano's theorem states that if
is a continuous function in the closed interval
with
and
of opposite sign, then there is a
in the open interval
such that
.
Contributed by:
Julio Cesar de la Yncera
SNAPSHOTS
DETAILS
Snapshot 1: The function is positive in the interval and therefore
for all
in
.
Snapshot 2: The function is negative in the interval so
for all
in
.
Snapshot 3: The function is positive for
and negative for
, therefore there is a
in
such that
.
RELATED LINKS
Bolzano's Theorem
(
Wolfram
MathWorld
)
Bolzano-Weierstrass Theorem
(
Wolfram
MathWorld
)
Weierstrass Intermediate Value Theorem
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Bolzano's Theorem
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/BolzanosTheorem/
Contributed by:
Julio Cesar de la Yncera
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