# Oscillation (mathematics)

In mathematics, oscillation is the behaviour of some sequences, or a function, that does not converge, but also does not diverge to +∞ or -∞; that is, oscillation is the failure to have a limit.

For example, the sequence 1, −1, 1, −1, 1, −1, ... does not converge to a limit, but remains bounded. In this case the sequence is periodic, and any sequence that is periodic without being constant will oscillate. On the other hand, oscillation doesn't imply periodicity.

Geometrically, an oscillating function on the real numbers follows some path in a space, without settling into ever-smaller regions. In well-behaved cases the path might look like a loop coming back on itself, that is, periodic behaviour; in the worst cases quite irregular movement covering a whole region.

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