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Intermediate value theorem

In mathematical analysis, the intermediate value theorem states that if f {\displaystyle f} is a continuous function whose domain contains the interval and s {\displaystyle s} is a number such that f ( a ) < s < f ( b ) {\displaystyle f(a)<s<f(b)} , then there exists some x {\displaystyle x} between a {\displaystyle a} and b {\displaystyle b} such that f…

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Overview

Motivation

Theorem

Proof

History

Darboux functions

Generalizations

In constructive mathematics

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Intermediate value theorem

Nodes66
Edges65
Triples68
Avg. degree1.97
Density0.030303
Components1

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Intermediate value theorem

Top relations

related to External links · 16
Intermediate value theorem → Belk, Bolzano Theorem, Eric, Intermediate, January, Jim, Julio Cesar, MathWorld, Mizar, Stack Exchange, T4, Theorem, Two-dimensional, Weisstein, Wolfram Demonstrations Project, Yncera
related to history · 13
Intermediate value theorem → Augustin-Louis Cauchy, BCE, Before, Bernard Bolzano, Bolzano, Both, Bryson, Heraclea, Joseph-Louis Lagrange, Louis Arbogast, Proponents, Simon Stevin, The
has application · 8
Intermediate value theorem → Borsuk, Define, Draw, Due, Euclidean, If, Take, Ulam
related to Multi-dimensional spaces · 8
Intermediate value theorem → Dn, Intermediate, Let, Let Dn, Rn, Suppose, The Poincaré-Miranda, Vrahatis
related to Darboux functions · 7
Intermediate value theorem → Another, As, Conway's, Darboux, However, The, This
related to Proof · 5
Intermediate value theorem → Despite, For, However, The, Weierstrass Nullstellensatz
related to In constructive mathematics · 4
Intermediate value theorem → In, Instead, Let, Then
related to Theorem · 3
Intermediate value theorem → Consider, The, Then
is a · 2
Intermediate value theorem → Borsuk, immediate consequence of these two properties of connectedness
related to General metric and topological spaces · 2
Intermediate value theorem → If, The

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displaystyle theorem value intermediate continuous function interval delta property exists varepsilon real functions set version numbers connected points every must

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SubjectPredicateObjectConfidenceSrc
Intermediate value theoremis aBorsuk0.90text
Intermediate value theoremis aimmediate consequence of these two properties of connectedness0.90text
Intermediate value theoremhas applicationBorsuk0.60section
Intermediate value theoremhas applicationUlam0.60section
Intermediate value theoremhas applicationEuclidean0.60section
Intermediate value theoremhas applicationTake0.60section
Intermediate value theoremhas applicationDraw0.60section
Intermediate value theoremhas applicationDefine0.60section
Intermediate value theoremhas applicationIf0.60section
Intermediate value theoremhas applicationDue0.60section
Intermediate value theoremrelated to Darboux functionsDarboux0.60section
Intermediate value theoremrelated to Darboux functionsThe0.60section

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