Definition in Hyperreal Numbers
The definition of the limit using the hyperreal numbers formalizes the intuition that for a "very large" value of the index, the corresponding term is "very close" to the limit. More precisely, a real sequence tends to L if for every infinite hypernatural H, the term xH is infinitely close to L, i.e., the difference xH - L is infinitesimal. Equivalently, L is the standard part of xH
- .
Thus, the limit can be defined by the formula
where the limit exists if and only if the righthand side is independent of the choice of an infinite H.
Read more about this topic: Limit Of A Sequence
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