Mathematics Atlas

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Continuity

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Unbroken Smooth Curve

A continuous function is one where a small variation of its argument induces at most a small variation of its value, so that the function has no abrupt jumps or breaks. Bernard Bolzano gave a form of the epsilon-delta definition of continuity in 1817.

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1817 1
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1. Continuous Function (Wikipedia)
Wikimedia Foundationlead paragraph
Quote, lead paragraph
a small variation of its argument induces at most a small variation of its value. This implies there are no abrupt changes in value, known as discontinuities.
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1. Continuous Function (Wikipedia)
Wikimedia FoundationHistory section
Quote, History section
A form of the epsilon-delta definition of continuity was first given by Bernard Bolzano in 1817.
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Augustin-Louis Cauchy (Wikipedia)
Wikimedia FoundationAssociated With: Augustin-Louis Cauchy, lead paragraph
Quote, Associated With: Augustin-Louis Cauchy, lead paragraph
He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real analysis)
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