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===Limit===
Given a sequence <math>(u_n)</math>, its limit is defined by <math>\lim_{n\to\infty}u_n=\text{st}(u_H)</math> where <math>H\in{}^\ast\mathbb{N}\setminus\mathbb{N}</math> is an infinite index. Here the limit is said to exist if the standard part is the same regardless of the infinite index chosen.
===Continuity===
A real function <math>f</math> is continuous at a real point <math>x</math> if and only if the composition <math>\text{st}\circ f</math> is ''constant'' on the [[halo (mathematics)|halo]] of <math>x</math>.
==See also==
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