At 1:45 PM -0500 2/2/98, Patrick Logan wrote:

[snip]

>
>(3) Point is a two-dimensional value. It cannot be made linear.

(I'm assuming that by 'linear' one means 'having a one-to-one
correspondence with the natural numbers'.)

(Smalltalk) points are ordered pairs of integers (not of reals), correct?
Thus, they have a mapping to the rationals.

	1 at 1 --> 1/1
	1 at 2 -->	1/2
	1 at 3 --> 1/3
	etc.

Since the rationals are denumerable, there is a mapping from them onto the
naturals, and therefore there is a mapping from points onto the naturals,
i.e., a linear ordering...

....though, admittedly, not the most practical ordering, but it's pretty
easy to rearrange things so they come out more useful.r

(Given that points are most often, I would guess, used in finite rows,
there is a very useful set of linear orderings, 1 at 1 < 1 at 2 ... < 1 at m < 2 at 1
.... which is implemented by Travis' sort block, I believe.)

Or did I misunderstand your point (either the argumentative one, the
Smalltalk one, or the mathematical one ;)?

[snip]

Cheers,
Bijan Parsia