Non-standard Calculus - Limit of Sequence

Limit of Sequence

Given a sequence of real numbers, if we say L is the limit of the sequence and write

if for every infinite hypernatural n, we have st(xn)=L (here the extension principle is used to define xn for every hyperinteger n).

This definition has no quantifier alternations.The standard (ε, δ)-style definition on the other hand does have quantifier alternations:

Read more about this topic:  Non-standard Calculus

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