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
Famous quotes containing the words limit of, limit and/or sequence:
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I never spent an hour’s talk withal.”
—William Shakespeare (1564–1616)
“It is after all the greatest art to limit and isolate oneself.”
—Johann Wolfgang Von Goethe (1749–1832)
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—Walter Benjamin (1892–1940)