as representing the set of all functions that satisfy One can then equivalently write read as "the function is among the set of all functions of

Examples with an infinite domain

In typical usage the notation is applied to an infinite interval of real numbers and captures the behavior of the function for very large . In this setting, the contribution of the terms that grow "most quickly" will eventually make the other ones irrelevant. As a result, the following simplification rules can be applied:
*If is a sum of

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