[Blindmath] Basic mathematical concept question

[Andrew Stacey]

On Sat, Mar 24, 2012 at 03:17:15PM -0500, Richard Baldwin wrote:
>    Now for the practical.
> 
>    Many real-life "curves" cannot be analytically defined in precise
>    mathematical terms without using an infinite series.

In light of your first (fantastic) email on this, I'd like to point out that
this holds for almost all functions.  The only functions that can be precisely
defined are polynomials with rational coefficients.  Everything else exists
only as an approximation.  We name those functions that we encounter
frequently, but that doesn't mean that we know any more about them - in
particular, about their values - than about functions which we only define
implicitly or by some weird integral formula.

Andrew