I make the painfully (for you) lazy proposition of N=0 and P to W being any perfect squares you please. ... ...
7935
adh_math
Jun 10, 2004 9:54 pm
... Presumably "number" means "positive integer" in this context. :) There are infinitely many examples N=P=...=W=2k^2 (k a positive integer), but perhaps the...
7936
adh_math
Jun 10, 2004 10:17 pm
... or ... Remarkably, the answer is the same either way. So as not to spoil anyone's fun, I won't post the solution. (Martin Gardner's "Aha! Insight" contains...
7937
pdiibq
Jun 11, 2004 12:37 am
I found this a long time ago. Check it out. http://www.mycathatesyou.com...
7938
Vijay
v0121223
Jun 11, 2004 7:14 am
Can we find a homomorphism which is neither Injective nor Surjective ? Substantiate. __________________________________ Do you Yahoo!? Friends. Fun. Try the...
7939
Julien
julien_santini
Jun 11, 2004 7:45 am
... The answer is Yes. Now i let you find an example (that must be really easy, especially for the surjective part; for the injective part, refer to the first...
7940
clooneman
Jun 11, 2004 12:54 pm
It's a good guess that the game goes down tot eh wire and is only decided after the last number is chosen. ... The ... zero?...
7941
clooneman
Jun 11, 2004 12:58 pm
Hilarious. But to hell with the cats, that clock is the coolest fucking thing I've ever seen!!!...
7942
clooneman
Jun 11, 2004 1:01 pm
Qu'est-ce que c'est une homomorphisme?...
7943
Julien
julien_santini
Jun 11, 2004 1:53 pm
... Just another word to say morphism....
7944
clooneman
Jun 11, 2004 4:42 pm
In the way, say, 4 might change into 5? Or is that a metamorphosis?...
7945
Adam
a_math_guy
Jun 11, 2004 6:44 pm
The trivial homomorphism works well : f : any group/ring/field G -> (additive) identity within any group/ring/field F. If you want a non- trivial example then...
7946
adh_math
Jun 12, 2004 3:09 pm
... Roughly, a (homo)morphism is a mapping that preserves some structure. The concept presupposes having two sets with additional structure. :) A "group" is an...
7947
Julien
julien_santini
Jun 12, 2004 3:25 pm
... structure. ... structure. :) ... Yes, precisely. In the most general setting, we define a category i.e a set of objects O such that for any A,B in O, there...
7948
Sudarshan Iyengar
sudarshansr
Jun 13, 2004 7:07 am
Is there a transformation from R-->R^2 where in the real line gets transformed onto an open disk in R^2 say x^2+y^2<1 In other words :- Is it impossible for us...
7949
Julien
julien_santini
Jun 13, 2004 7:30 am
... R and {(x,y);x^2+y^2<1} are trivially equipollent (you can find a bijection between them) because they have same cardinal. That answers your question ......
7950
Sudarshan Iyengar
sudarshansr
Jun 13, 2004 4:21 pm
Hi, thanks for the instantaneous response. well what exactly is the bijection that you can think of from R to the unit open disk? I don't think its possible!...
7951
Sudarshan Iyengar
sudarshansr
Jun 13, 2004 4:21 pm
Hi, thanks for the instantaneous response. well what exactly is the bijection that you can think of from R to the unit open disk? I don't think its possible!...
7952
Julien
julien_santini
Jun 13, 2004 6:08 pm
... Yes it is ... Generally the proof of Cantor (Schroeder) - Bernstein theorem helps you find *systematically* explicit bijections between two equipollent...
7953
mansoor
mansoor_165
Jun 14, 2004 6:03 am
Prove that all the prime numbers are of the form 4*n+1 or 4*n+3. Mansoor....
7954
Julien
julien_santini
Jun 14, 2004 7:27 am
... Could a prime be of the form 4n+2 or 4n+4 ? The non-trivial question you should set yourself is: Prove that there exist infinitely many primes of the form...
7955
Vijay
v0121223
Jun 14, 2004 8:27 am
of course , there are infinitely many primes of the form 4n+1 and 4n+3.and you can prove it by supposing the contrary that there are only finitely many primes ...
7956
Julien
julien_santini
Jun 14, 2004 9:13 am
... Showing that there are infinitely many primes of the form 4n+1 or 4n+3 or 6n+5 or 8n+5 are simple exercises. But the extension you mentioned (known under...
7957
clooneman
Jun 14, 2004 12:23 pm
First of all, 2 is of neither form. Secondly, all ODD numbers are of the form 4*n+1 or 4*n+3, so that more or less wraps that one up....
7958
eskay s
peeskay
Jun 14, 2004 1:13 pm
This may sound simple but boggling , can u say what are the times the minutes and hour hands meet in 12 hrs, may be easily we could come to a solution but...
7959
adh_math
Jun 14, 2004 2:06 pm
... Though Julien has answered, here are a couple of tangential comments and (undergraduate-level:) questions under the assumption of continuity: 1. The...
7960
Ayyoub
aalqaissi
Jun 14, 2004 2:50 pm
Assume the following h:Hour m:Minute then m=5h+(1/12)m or (11/12)m=5h my result is: h m -- ----- 01 05.45 02 10.91 03 16.36 04...
7961
Julien
julien_santini
Jun 14, 2004 5:06 pm
... And generally, the Hahn-Mazurkiewicz theorem tells you that there is a continuous mapping from [a,b] to A (where A is a topological subspace of a Hausdorff...
7962
pdiibq
Jun 15, 2004 3:47 am
I found an equation that gives all primes and I improved on it slightly, but I need help solving for a variable. The link is ...
7963
Dimitri Vorkapich (Di...
xirja
Jun 15, 2004 7:11 pm
Hi, Following is a link to an equation I discovered. I recently began work in 3d and was blown away by this and wanted to share it and get feedback to see if...
