... This is what I had: 0 = {} 1 = {0} = {{}} since 0 = {} 2 = {0,1} = {{},{{}}}, since 0 = {} and 1 = {{}} 3 = {0,1,2} = {{},{{}},{{},{{}}}}, since ... ... ...
... Okay, let me give it a try. Our universe U = [0,1] is the set of real numbers between 0 and 1, including endpoints. A word w is a subset of U. Thus, the...
... T0 and T1, as well as T2, T3, and T4, are standard terms in topology, see: http://mathworld.wolfram.com/SeparationAxioms.html My recollection from grad...
hi mark. thanks for the reformulation without all the chugoo terminology (haha).. somehow the question can be stated in terms of a mapping of an infinite set...
Its really quite simple actually...the people dealing with the situation want to 'see' what is actually going on rather than dealing with what 'might' actually...
I'll be out of contact for a few days due to a family illness, but I wanted to put out some possible approaches to problem 1.5 before I leave. I really...
hi mark, I printed out many pages of material on VPs problem yesterday & today and also your own commentary & proof, & your rewrite of it I find extremely...
... Comonoids are closed under finite ANDs and ORs (Lemmas 1 and 2 from problem 1.2), and Chu spaces (= dictionaries) that are closed under arbirary ANDs and...
In einer eMail vom 31/01/03 10:10:19 PM (MEZ) Mitteleuropäische Zeit schreibt ... wouldn't it be astonishing if such a fundamental,short,simple question...
a moment of silence & some words for 7 dead astronauts http://www.wired.com/news/technology/0,1282,57519,00.html I was 16 years old, freshman in highschool ...
hi mark.. interesting.. I forgot to say--call the smallest dictionary associate with a crossword (with all extraneous words removed) "minimal". is it possible...
hi all. I credited VP awhile ago with the great & very substantial influence of his contest here, but it deserves to be mentioned again. on jan 1, the very 1st...
web services apparently key new area of big business competition eg sun,microsoft,ibm etc http://www.nytimes.com/2003/02/03/technology/03SOFT.html early...
Now that it's the weekend I get a chance to address some of the questions raised. Easiest first. ====================================================== 1....
Hi Vaughan, I don't know if Warren was very slyly answering your question, or if it was just serendipitous, but if you look at the way your original message...
... Then I could get a job with the NY Times making up impossible crossword puzzles. Will Shortz and I would go out for a beer after a hard day's puzzle...
Thanks, Kurt, I'll try replacing " " by ". " in future, which has the advantage of halving the number of annoying dots. The other solutions are less than...
Ah, the wonders of system incoherence. 'Tis a wonderful thing, and of course the sender doesn't know how to game the system into doing the right thing and the...
hi all. alas, the yahoo reformatting of ascii art here has bit us a lot in the past & its a real bummer. I am especially annoyed how it takes my perl code ...
yeeks, VP is really floating in the rarefied high atmosphere of abstraction.. not much oxygen up here ***gasp***. based mainly on the $500 prize, I dedicated...
Warren writes: See reply below. ... From: theory-edge@yahoogroups.com Date: Monday, February 03, 2003 10:36:42 AM To: theory-edge@yahoogroups.com Subject:...
... uncountable ... IMHO, What makes the problem for uncountable words/dictionaries important ,is that answering it will allow us to know exactly *why* the...
... Ok, so this philosopher comes along, defines a strange notion called a "continuum," and asks, does a continuum exist? And people work on this for a while...
... Fair question. There are actually two notions, tensor product A*B and function space ("internal hom" as category theorists call it) A-oB. The latter is...
if I time this right, it is theory-edge msg #7000. and now the numerous beautiful and luscious theory-edge babe groupies, all dressed in bikinis, are squeezing...
