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Everything about Intermediate value theorem
Continuous function on an interval takes on every value between its values at the ends
In mathematical analysis, the intermediate value theorem states that if is a continuous function whose domain contains the interval [a, b] and is a number such that, then there exists some between and such that. That is, the image of a continuous function over an interval is itself an interval that contains. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Intermediate value theoremA 5-minute orientation
- Skim a recent paper: Connecting algorithmics to mathematics learning: a design study of the intermediate value theorem and the bisection algorithmInfluential work since 2022
- Pick up a classic book: Beginning & Intermediate AlgebraThe most-reprinted book on the subject
- Read the landmark paper: A translation of Bolzano's paper on the intermediate value theoremCited 65 times
- Go sideways: Continuous functionA closely related topic
- Go sideways: Extreme value theoremA closely related topic
đź“– Definitions
Noun A theorem that states for each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
A translation of Bolzano's paper on the intermediate value theorem
An intermediate value theorem for monotone operators in ordered Banach spaces
The binary expansion and the intermediate value theorem in constructive reverse mathematics
A General Constructive Intermediate Value Theorem
From Intermediate Value Theorem To Chaos
Intermediate Value Theorem for Analytic Functions on a Levi-Civita Field
Bernoulli convolutions and an intermediate value theorem for entropies ofK-partitions
Teaching the Representations of Concepts in Calculus: The Case of the Intermediate Value Theorem
🆕 Influential since 2022
Connecting algorithmics to mathematics learning: a design study of the intermediate value theorem and the bisection algorithm
The Intermediate Value Theorem and Decision-Making in Psychology and Economics: An Expositional Consolidation
An infinite dimensional version of the intermediate value theorem
Quasi-intermediate value theorem and outflanking arc theorem for plane maps
The Tate Intermediate Value Theorem
đź“š Books worth reading
Beginning & Intermediate AlgebraK. Elayn Martin-Gay · 2001
Cartesian meditationsEdmund Husserl, Dorion Cairns · 1960
Intermediate algebra for college studentsRobert Blitzer · 2009
First-year calculusEinar Hille · 1968
Intermediate AnalysisNorman B. Haaser, Joseph P. LaSalle · 1964
How We Got from There to HereEugene Boman · 2014
The Best Writing on Mathematics 2014Mircea Pitici · 2014
A youtube Calculus Workbook (Part I)Frédéric Mynard New Jersey City University · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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