What's the point of non-standard analysis?

- it's natural and intuitive:
  it formalizes Leibniz's notion of infintesimals

- it often reduces quantifiers:
[Quotes Robinson's "Metamathematical Problems"]
Rather than saying that:
$\lim_{n\to \infty} s_n = 0$
means:
$\forall \epsilon > 0 \exists N \in \bN \forall n > N
 \abs{s_n} < \epsilon$
in standard language,
in non-standard language, it means
``for all infinite natural $n$, $s_n$ is infintesimal''
...it replaces 2 of the 3 quantifiers with the use of new predicates.

- it's a cool application of model theory

- it gives new insight
  (but is equivalent to the standard theory, natch)
