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.](/Images/godic/202501/31/LimSup.svg4200.png")
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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).