File:Illustration_for_the_intermediate_value_theorem.svg · Wikimedia Commons · See Wikimedia Commons
In the Vinony graph
Vinony's link graph records 98 inbound references to 介值定理, and connects out to Darboux's theorem, interval and image.
It sits within the topics Theorems in calculus, Theorems in real analysis and Theory of continuous functions.
Vinony links it to 34 Wikipedia language editions.
Wikidata facts
- Instance of
- theorem
- Part of
- list of theorems
- Named after
- Jean Gaston Darboux
- Image
- Illustration for the intermediate value theorem.svg
Show 4 more facts
- short name
- TVI
- Commons category
- Intermediate value theorem
- maintained by WikiProject
- WikiProject Mathematics
- studied by
- calculus
Sources (2)
via Wikidata · CC0
Article · 中文
在数学分析中，介值定理（英語：intermediate value theorem，又稱中間值定理）描述了連續函數在兩點之間的連續性： 假設有一連續函數 ，且假設 ，若對任意數 滿足 ，則存在一點 ，使得，當 時也有類似敘述。 直觀地比喻，這代表在區間上可以畫出一個連續曲線，而不讓筆離開紙面。或者可以這樣說，函數的圖像必然會穿過區間中的每一個點。 介值定理首先由伯纳德·波尔查诺在1817年提出和证明，在這個證明中，他附帶證明了波爾查諾－魏爾斯特拉斯定理。
Abstract from DBpedia / Wikipedia · CC BY-SA
Gallery (2)
Connections
Darboux's theorem
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interval
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image
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connected space
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International Standard Book Number
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mathematical analysis
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function
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real number
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topology
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rational number
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set
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digital object identifier
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Joseph-Louis Lagrange
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International Standard Serial Number
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derivative
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irrational number
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polynomial
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Augustin-Louis Cauchy
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continuous function
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JSTOR
Organization