Math

using geometry to show why there is a Infinitude of Primes proof but no Twin Primes possible #617 Correcting Math
Let me recap what this adventure is plunging into. We notice the old math system never defined with precision the difference between a finite number and an infinite number. So that 3 is a Peano axiom number as well as 3333....33333. So the next question was, since the old math is so poor in definitions, cannot ... 30 Jun 2010 22:01

Modularity of Mind
Modularity of mind is the notion that a mind may, at least in part, be composed of separate innate structures which have established, evolutionarily developed functional purposes. Proponents believe this view is implied by Noam Chomsky's concept of a universal, generative grammar. Such universal features of languag... 1 Jul 2010 12:14

(phi( <[1] 2 3 4...> ) & An (phi ( <[1 2 ... n] n+1 n+2 ...>) -> phi( <[1 2 ... n n+1] n+2 n+3 ...> ))) -> phi( <[1 2 3 4...]> )
Behold the Cantor killer! phi( <[1] 2 3 4...> ) & An (phi ( <[1 2 ... n] n+1 n+2 ...>) -> phi( <[1 2 ... n n+1] n+2 n+3 ...> )) -> phi( <[1 2 3 4...]> ) Prefix Induction Schema If a property holds for the 1st element in a sequence, and if it holds for the first n elements in a sequence then it holds f... 30 Jun 2010 22:01

How Can ZFC/PA do much of Math - it Can't Even Prove PA isConsistent (EASY PROOF)
herbzet <herbzet(a)gmail.com> writes: This is what I was getting at, and where I found your reply to billh04 somewhat lacking. Billh04 asked Are you saying that it is a theorem of ZFC that PA is consistent? I answered that, yes, this is indeed the case. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi... 30 Jun 2010 22:01

JSH: Discrete log solution and degrees of freedom analysis
I've noted a way to solve for m, when k^m = q mod N, through integer factorization, which is then an approach to solving discrete logarithms in a prior post. In this post I'll explain when the equations MUST work, where a simple analysis can be done trivially using methods familiar to those who've solved simultane... 7 Jul 2010 16:47

New Differential Equation website
A Website Devoted to Differential Equations A couple of months ago we posted a message here to announce the availability of a new website, devoted to the subject of Differential Equations, and whose goal will be to present that subject in an as an intuitive and conceptual a way as possible. The URL is: ... 1 Jul 2010 17:51

Missouri State University Problem Corner (new address)
The new problems (High School, Advanced, and Challenge) have been posted. Our new address is http://people.missouristate.edu/lesreid/POTW.html Please make a note of it. ... 30 Jun 2010 16:30

Unique Prime Factorization theorem is also in the Indirect method #615 Correcting Math
Archimedes Plutonium wrote: (snipped all else) INDIRECT (contradiction) Method, Long-form; Infinitude of Primes Proof and the numbering is different to show the reductio ad absurdum structure as given by Thomason and Fitch in Symbolic Logic book. (1) Definition of prime as a positive ... 30 Jun 2010 16:30

Statistical Significance and When to Stop a Simulation?
Hi, I'll be writing a program to simulate Blackjack play, and I have a question or two about how long to run a simulation. It is related to the following question ... assume that I have a fair coin that I toss a large number of times, and assume that I calculate the number of heads and tails and that I main... 1 Jul 2010 13:21

What Else Can I Do With Modulus?
In the integer domain, given c = pq, where p and q are prime and > 0, and given integer modulus m > 1, the following is true: c mod m = (pq) mod m = (p mod m)(q mod m) Are there any other non-equivalent equalities involving p, q, c and m? Any references, on-line or otherwise, are welcome. Thanks for readin... 14 Jul 2010 15:26