Non-standard Calculus - Limit

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.