Jim Choate <ravage@EINSTEIN.ssz.com> writes:

In reference to numbers which you can't describe, if you examine the work they are ALL in the Complex domain, none of them are Real's.

Only countably many real numbers, or members of any uncountable set, are denumerable. It is the property of being uncountable, rather than of being real or complex, which is important here. In general, only countably many members of any uncountable set can be precisely specified within any formal system, given names comprised of strings of symbols, or other similar things.

Complex numbers deal with areas, not with lengths.

It is often convenient, such as when drawing contour maps, to consider the complex numbers to be in 1-1 correspondence with the points of the plane. However, I wouldn't necessarily consider regions of the complex plane to have "area" in the Euclidian sense.

If there existed a Real for which we could not describe this would imply that we could not draw a line of that length.

We can't physically draw a line segment to arbitrary high precision. We can conceive of the notion of line segments being in 1-1 correspondence with the reals, but we can specify at most countably many "finitely denumerable" line segments if we wish to discuss their lengths individually. -- Mike Duvos $ PGP 2.6 Public Key available $ mpd@netcom.com $ via Finger. $