... It seems to me, if there is "at least" one apple between any two oranges, and "at least" one orange between any two apples, then, there are equal numbers...
1028
Mikhail Adigeyev
madi@...
Feb 1, 2000 3:05 pm
... No, you are not right. There is an infinite set of rational numbers between any two irrational numbers, and vice versa. And when we "count" infinite sets,...
1029
Darren Naylor
darren.naylor@...
Feb 1, 2000 3:18 pm
You should note that the decimal expansion of an irrational eventually repeats itself. e.g, 25/198 = 0.126262626... So if you were to pick a real number at...
1030
Kaushik Sridharan
kaushik@...
Feb 2, 2000 7:14 am
... English ... There is ... proof in ... briefly. ... This page here describes the concept of infinity and the difference in cardinality between the sets of...
1031
Kaushik Sridharan
kaushik@...
Feb 2, 2000 8:58 am
... You mean 'rational', of course! Kaushik...
1032
d p
danpeh@...
Feb 2, 2000 11:12 am
"I didn't come here for an argument!" "Yes, you did." Hi Mikhail, First of all, let me state that my own expertise is in counting FINITE sets, mostly described...
1033
Klaus D. Witzel
kwitzel@...
Feb 2, 2000 12:57 pm
Let me give an example of an "infinite" construct for which my (p:qr) system can count the number of {satisfying} solutions: f(p:(q:f~q)~p) Here, f is a...
1034
Darren Naylor
darren.naylor@...
Feb 2, 2000 1:38 pm
"kaushik sridharan" <kaushi-@...> wrote: original article:http://www.egroups.com/group/theory-edge/?start=1031 ... eventually ... random ... itself ... ...
1035
SuperRyan@...
Feb 2, 2000 10:27 pm
In a message dated 2/2/2000 6:19:04 am Eastern Standard Time, ... The relation of height to atoms is quite different from the relation between set size and set...
1036
d p
danpeh@...
Feb 3, 2000 9:36 am
Thanks Ryan. Do you remember the #P=#Q theorem: The number of satisfying assignments to a boolean expression is equal to the number of valid quantifications of...
1037
Mikhail Adigeyev
madi@...
Feb 3, 2000 2:58 pm
Hi Dan. ... Well, I didn't intend to insult you somehow :-) You've asked, I've answered, thats all. And I ask you to apologize me for mistakes/misspellings in...
1038
Mikhail Adigeyev
madi@...
Feb 4, 2000 8:32 am
... Well, you should add that between any 2 x's there is one more x :-) Mikhail Adigeyev madi@......
1039
d p
danpeh@...
Feb 4, 2000 4:27 pm
Dear Mikhail, Thank you for your comprehensive replies! I appreciate them quite alot. Pardon me for trimming them in the following, in an attempt to get to...
1040
Vladimir Z. Nuri
vznuri@...
Feb 5, 2000 4:15 am
while I am overjoyed at any kind of sustained input to this list, especially that which does not require my own cheerleading, this subject is stretching the...
1041
Vladimir Z. Nuri
vznuri@...
Feb 5, 2000 4:25 am
hi everyone-- a note to Dan: yes, Davis Putnam examines the ways to solve a boolean formula. what is interesting and highly relevant however imho is that DP...
1042
Vladimir Z. Nuri
vznuri@...
Feb 5, 2000 4:28 am
hi Klaus, I continue to be intrigued by your p:qr system and think it is great you are exploring it. you seem to have some tantalizing results. I was wondering...
1043
Vladimir Z. Nuri
vznuri@...
Feb 5, 2000 4:38 am
From: "=?ISO-8859-1?Q?"=F7=F8=EF_=E5=E5=EC=F3"_" <wolffund@...> Subject: Wolf Prize 2000 in Mathematics Date: Wed, 26 Jan 2000 17:13:23 +0200 To:...
1044
Klaus D. Witzel
kwitzel@...
Feb 5, 2000 10:52 am
Hi Vlad, from my view as an insider to (p:qr) I'm rather preoccupied wrt "most" remarkable theorem(s), albeit there are a few I have (as yet?) not found in ...
1045
SuperRyan@...
Feb 7, 2000 9:00 pm
In a message dated 2/3/2000 4:41:22 am Eastern Standard Time, ... There is an old newsgroup post in which this precise thing is done. See comp.theory on...
1046
Frode L. Odegard
frode@...
Feb 7, 2000 10:45 pm
This is probably too late (application deadline today!) but it might be interesting for people here to read about nevertheless. 2000 Complex Systems Summer...
1047
d p
danpeh@...
Feb 8, 2000 6:17 pm
Ryan, Fine, fine. Forget about rationals and irrationals for a moment. Consider two infinite sets, X, and Y. They are different sets, of different things...
1048
d p
danpeh@...
Feb 8, 2000 6:59 pm
Ryan, I will stick to finities, of which I have a decent grasp. ... For everyone else's benefit, this part of the discussion is about the relationship between...
1049
Vladimir Z. Nuri
vznuri@...
Feb 10, 2000 6:53 am
From: Peter Cholak <cholak@...> Subject: Computability Prize (fwd from Richard Epstein) Date: Thu, 4 Nov 1999 11:39:20 -0500 To: COMP-THY@... ...
The two sets you describe have a simple model: draw a circle, halve it north-south with a single line, repeat the last step west-east. Label the points where...
1052
d p
danpeh@...
Feb 10, 2000 11:01 am
... I agree. The two sets I described CAN exist, and the rationals and irrationals are a model, but there are others too. A simpler model uses only the...
1053
Klaus D. Witzel
kwitzel@...
Feb 10, 2000 3:10 pm
"d p" <danpeh@...> wrote ... Of course there is, simply because no-one AFAIK has ever proved something non-trivial about the rationals / irrationals...
1054
d p
danpeh@...
Feb 11, 2000 10:52 am
Gee, this #P = #Q stuff sounds really hot. Is anyone else anywhere in the world studying it, or interested in it? ... First of all, it is an equality in and...
1055
Klaus D. Witzel
kwitzel@...
Feb 11, 2000 11:27 am
... Besides the obvious, your #P = #Q stuff is what makes me read & write in theory-edge! ... Not any longer: I want to be able to construct these fabolous Q...
1056
dan
danpeh@...
Feb 15, 2000 1:43 pm
Well, not much action for a few days. What gives, anyway? Temporal problems, or what? Well, I hosed my own email account pretty well. As you may have heard,...
