Oscillation (mathematics)

（重定向自Oscillating sequence）

Oscillation of a sequence (shown in blue) is the difference between the limit superior and limit inferior of the sequence.

sin (1/x) (the topologist's sine curve) has oscillation 2 at x = 0, and 0 elsewhere.

In mathematics, the oscillation of a function or a sequence is a number that quantifies how much a sequence or function varies between its extreme values as it approaches infinity or a point. As is the case with limits there are several definitions that put the intuitive concept into a form suitable for a mathematical treatment: oscillation of a sequence of real numbers, oscillation of a real valued function at a point, and oscillation of a function on an interval (or open set).

单词	Oscillating sequence
释义	Oscillating sequence 英语百科 Oscillation (mathematics) （重定向自Oscillating sequence） In mathematics, the oscillation of a function or a sequence is a number that quantifies how much a sequence or function varies between its extreme values as it approaches infinity or a point. As is the case with limits there are several definitions that put the intuitive concept into a form suitable for a mathematical treatment: oscillation of a sequence of real numbers, oscillation of a real valued function at a point, and oscillation of a function on an interval (or open set).
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