
Infinite is easier than big - ColinWright
http://www.johndcook.com/blog/2010/09/09/infinite-is-easier-than-big/
======
ColinWright
Two specific cases:

The Fourier transform can be thought of as representing a point in infinite
dimensional space as the amounts of each component. The sine and cosine waves
are orthogonal (in a technical sense) and of "unit length" (in a technical
sense), and all we're doing is, for a given "point" (function) in our vector
space we're finding out how much of X, how much of Y, _etc,_ is in that
vector.

Second example, Goodstein's theorem is trivial to prove if you use transfinite
arithmetic, but has (some claim) been shown to be independent of the Peano
Axioms, and hence impossible to prove with finitary methods. (There is also a
claimed proof. If both of these are true the Peano's Axioms are inconsistent)

Sometimes the infinite is easier than the finite.

