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@1 --> 1/1 1@2 --> 1/2 1@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@1 < 1@2 ... < 1@m < 2@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