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:
“An educational method that shall have liberty as its basis must intervene to help the child to a conquest of liberty. That is to say, his training must be such as shall help him to diminish as much as possible the social bonds which limit his activity.”
—Maria Montessori (1870–1952)
“It is after all the greatest art to limit and isolate oneself.”
—Johann Wolfgang Von Goethe (1749–1832)
“Moreover, the universe as a whole is infinite, for whatever is limited has an outermost edge to limit it, and such an edge is defined by something beyond. Since the universe has no edge, it has no limit; and since it lacks a limit, it is infinite and unbounded. Moreover, the universe is infinite both in the number of its atoms and in the extent of its void.”
—Epicurus (c. 341–271 B.C.)