There are many circumstances in mathematics in which one has an object of one kind and one would like to approximate it by an object of a different kind, or a more specific kind. It is not clear that any single piece of advice applies to all such circumstances, so this article contains links to articles about more specific kinds of approximation.

If the number of links in this page gets too big, then a new level in the hierarchy will be needed.

Approximating functions by polynomials

Approximating functions by better behaved functions

To prove abstractly that a function of one kind can be approximated by a function of another, try the Hahn-Banach theorem

Approximating real numbers by rational numbers

Approximating continuous structures by discrete structures