Logic
in [Science]
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Methods of Proving all of Incompleteness in Logic in Trivially Short Proofs & a Challenge There are various ways in which we can prove the 3 fundamental results of Incompleteness in Logic (Godel 1931, Rosser 1936, Smullyan 1961) in a simple, almost trivial, proof. The entire proof is very short, but may be completely dominated by self reference. This is in contrast to published proofs which are many... 30 May 2010 01:31
New Anti-Cantor Attack |-|ercules says... Cantor's second proof of 'uncountable infinity' is based on trying to >enumerate the powerset of naturals. [stuff deleted] Here's my equivalent proof of uncountable infinity. This is an instance of a general theorem: for every correct proof, there exists an incorrect proof that look... 5 Jun 2010 02:47
Meami.org Publishes Polynomial Time Quicksort Algortihm: [[in-place]] partition algorithm and can achieve the complete sort using <math>O(\log n)</math> space (not counting the input) use on average (for the [[call stack]]): '''function''' partition(array, left, right, pivotIndex) pivotValue := array[pivotIndex] swap array[pivotIndex] and array[right] ... 30 May 2010 19:47
Question about Hugh Woodin's original proof of projective determinacy. On 05/29/10 03:41, Rupert wrote: I think I might have asked this before. In his article "The Continuum Hypothesis, Part I" Hugh Woodin writes "In 1978 Martin succeeded in proving the determinacy of all boldface Sigma^1_2 sets using essentially the strongest large-cardinal hypothesis known at the ... 29 May 2010 19:02
Dawkins on Turing In Radio Times for 29 May to 4 June, Richard Dawkins is quoted: If anyone could be said to have invented the future it was Alan Turing. He created a wartime code-breaking machine that was the basis for all computer technology. By imagining a machine that could solve all conceivable mathematical ... 1 Jun 2010 16:24
The fundamental problem with Godels theorems- why the first and second theorems end in paradox colin leslie dean points out The fundamental problem with Godels theorems are he creates an imprdeicative statement and the theorems apply to themselves ie are impredicative- thus leading to paradox ieie this is godels impredicative statement used in his first theorem http://en.wikipedia.org/wiki/G%C3%B6del%27s_... 29 May 2010 23:22
Question about Hugh Woodin's original proof of projective determinacy. I think I might have asked this before. In his article "The Continuum Hypothesis, Part I" Hugh Woodin writes "In 1978 Martin succeeded in proving the determinacy of all boldface Sigma^1_2 sets using essentially the strongest large-cardinal hypothesis known at the time. Finally in 1983 I proved the determinacy ... 29 May 2010 03:53
Godels seconded theorem ends in paradox-simple proof colin leslie dean has shown Godels seconded theorem ends in paradox http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Proof_sketch_for_the_second_theorem [quote]The following rephrasing of the second theorem is even more unsettling to the foundations of mathematics: If an axiomatic system ca... 28 May 2010 01:47
Godels theorem ends in paradox-simply proof it is shown by colin leslie dean that Godels theorem ends in paradox it is said godel PROVED "there are mathematical true statements which cant be proven" in other words truth does not equate with proof. if that theorem is true then his theorem is false PROOF for if the theorem is true then truth does eq... 9 Jun 2010 15:20 |