Logic

Zugswang in my proof of No Odd Perfect Numbers #675 Correcting Math
Zugswang is easily seen in the picture proof of Pythagorean theorem where no words are needed to make the proof but only a picture of 3 squares resting on the sides of a right triangle, and with the other attending pictures. But my proof that No Odd Perfect Number exists is another Zugswang proof. It forces wi... 14 Jul 2010 16:32

zugswang concept in math Re: Proof of the Infinitude of Perfect Numbers and infinitude of Mersenne primes #674 Correcting Math
Archimedes Plutonium wrote: Alright, I am in no sort of rush. The proof of the Infinitude of Perfect Numbers has been waiting since Pythagoras of 3,000 years old, so what is 3 weeks more. When a new technique is found in mathematics that clears out a problem-- infinitude of Twin Primes and P... 14 Jul 2010 16:32

setting up a Math Induction template Re: Proof of the Infinitude of Perfect Numbers and infinitude of Mersenne primes #673 Correcting Math
Alright, I am in no sort of rush. The proof of the Infinitude of Perfect Numbers has been waiting since Pythagoras of 3,000 years old, so what is 3 weeks more. When a new technique is found in mathematics that clears out a problem-- infinitude of Twin Primes and Polignac Conjecture, you can usually bet that the... 14 Jul 2010 15:26

setting up a Math Induction template Re: Proof of the Infinitude of Perfect Numbers and infinitude of Mersenne primes #672 Correcting Math
Alright, I found a proof template for proving a broad class of prime sets whether they are infinite or not. The Twin Primes proof started it off and then the Polignac Conjecture was proved using the same technique of Indirect where W+1 and W-1 are necessarily prime. It works because the method delivers two necess... 14 Jul 2010 06:36

easy proof of No Odd Perfect number from simply 1/3 + 1/3 combo + 1/3 combo #671 Correcting Math
Archimedes Plutonium wrote: Archimedes Plutonium wrote: While I am at it, may as well jogg the memory of how sqrt2 is proven irrational as a tug of war between being even and odd: --- quoting from Wikipedia --- Assume that √2 is a rational number, meaning that there exists an inte... 14 Jul 2010 02:17

maybe able to prove No Odd Perfect number from simply 1/3 + 1/3 combo + 1/3 combo #670 Correcting Math
Archimedes Plutonium wrote: While I am at it, may as well jogg the memory of how sqrt2 is proven irrational as a tug of war between being even and odd: --- quoting from Wikipedia --- Assume that √2 is a rational number, meaning that there exists an integer a and an integer b in general such that... 14 Jul 2010 01:12

Math-induction to get 2^p -1 Re: Proof of the Infinitude of Perfect Numbers and infinitude of Mersenne primes #668 Correcting Math
Archimedes Plutonium wrote: Archimedes Plutonium wrote: Archimedes Plutonium wrote: (snipping) Infinitude of Twin Primes proof: (1) definition of prime (2) hypothetical assumption: suppose set of all primes is finite and 2,3,5, 7, 11, . ., p_n, p_n+2 is the ... 14 Jul 2010 01:12

improvement in Re: Proof of the Infinitude of Perfect Numbers and infinitude of Mersenne primes #667 Correcting Math
Archimedes Plutonium wrote: Archimedes Plutonium wrote: (snipping) Infinitude of Twin Primes proof: (1) definition of prime (2) hypothetical assumption: suppose set of all primes is finite and 2,3,5, 7, 11, . ., p_n, p_n+2 is the complete list of all the primes with ... 13 Jul 2010 17:32

related to sqrt2 irrational proof Re: Proof that 1 is the only Odd Perfect Number #666 Correcting Math
While I am at it, may as well jogg the memory of how sqrt2 is proven irrational as a tug of war between being even and odd: --- quoting from Wikipedia --- Assume that √2 is a rational number, meaning that there exists an integer a and an integer b in general such that a / b = √2. Then √2 can be writte... 13 Jul 2010 17:32

Proof that 1 is the only Odd Perfect Number #665 Correcting Math
While I am at it, I may as well clear out all the old unsolved Ancient Greek conjectures of these three: 1) Twin Primes 2) Infinitude of even Perfect Numbers 3) 1 is the only odd Perfect Number I proved Twin Primes and even Perfect Numbers already in this thread so may as well grapple with 1 is the only odd Pe... 13 Jul 2010 16:26