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:
“Berowne they call him, but a merrier man,
Within the limit of becoming mirth,
I never spent an hour’s talk withal.”
—William Shakespeare (1564–1616)
“... there are two types of happiness and I have chosen that of the murderers. For I am happy. There was a time when I thought I had reached the limit of distress. Beyond that limit, there is a sterile and magnificent happiness.”
—Albert Camus (1913–1960)
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—Walter Benjamin (1892–1940)