Limit
While the thrust of Robinson's approach is that one can dispense with the limit-theoretic approach using multiple quantifiers, the notion of limit can be easily recaptured in terms of the standard part function st, namely
if and only if whenever the difference x − a is infinitesimal, the difference ƒ(x) − L is infinitesimal, as well, or in formulas:
- if st(x) = a then st(ƒ(x)) = L,
cf. (ε, δ)-definition of limit.
Read more about this topic: Non-standard Calculus
Famous quotes containing the word limit:
“Can you find out the deep things of God? Can you find out the limit of the Almighty?”
—Bible: Hebrew, Job 11:7.
“Today one does not hear much about him.... The fame of his likes circulates briskly but soon grows heavy and stale; and as for history it will limit his life story to the dash between two dates.”
—Vladimir Nabokov (1899–1977)
“It is after all the greatest art to limit and isolate oneself.”
—Johann Wolfgang Von Goethe (1749–1832)