Cauchy Sequence - Generalizations - in A Hyperreal Continuum

In A Hyperreal Continuum

A real sequence has a natural hyperreal extension, defined for hypernatural values H of the index n in addition to the usual natural n. The sequence is Cauchy if and only if for every infinite H and K, the values and are infinitely close, or adequal, i.e.

where "st" is the standard part function.

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