Logic
in [Science]
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Why can no one in sci.math understand my simple point? Consider the list of increasing lengths of finite prefixes of pi 3 31 314 3141 ..... Everyone agrees that: this list contains every digit of pi (1) as pi is an infinite digit sequence, this means this list contains every digit of an infinite digit sequence (2) similarly, as computable digit sequ... 12 Jul 2010 05:15
Con this be done without invoking AC? The origin of this question comes from a colleague, who asked "Can you have two nonisomorphic rings R and S, such that the additive group of R is isomorphic to the additive group of S, and the multiplicative semigroup of R is isomorphic to the multiplicative semigroup of S"? My answer, after some thought, was "ye... 20 Jun 2010 22:15
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Beyond Incompleteness One way to "extend Rosser 1936" i.e. go beyond incompleteness, is to ask what purpose Rosser 1936 serves, and how else can we serve that purpose. The answer is, he (like Godel and Smullyan) refuted Hilbert's claims that the ideal Mathematical system is possible. How can we refute Hilbert in other ways? 1st.... 1 Jul 2010 21:10
Recursively Enumerable vs. Constructively Provable Is there a way to prove that some relation is r.e. without giving enough information to make the construction of a program to enumerate it obvious (extractable from the proof)? C-B ... 24 Jun 2010 14:09
How Can ZFC/PA do much of Math - it Can't Even Prove PA is Consistent (EASY PROOF) Charlie-Boo <shymathguy(a)gmail.com> writes: Since PA can't prove something as simple as that, how could anyone be so stupid as to claim ZFC/PA is a good basis for all of our ordinary math? Who makes this claim? You're hallucinating. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht spr... 14 Jun 2010 11:46
How Can ZFC/PA do much of Math - it Can't Even Prove PA is Consistent (EASY PROOF) ZFC/PA is supposed to do all ordinary mathematics*. But it is easy to prove that PA is consistent (its axioms and rules preserve truth) yet (by Godel-2) PA can't do such a simple proof as that. Since PA can't prove something as simple as that, how could anyone be so stupid as to claim ZFC/PA is a good basis fo... 12 Jul 2010 17:24
equivalence Â…the internal to the atom orbiting electron idea, reminds me of Einstein declaring that a uniform gravitational field is equivalent to acceleration. What is a uniform gravitational field? It is a field that acts on all objects in the same way. Gravity has us tied to the whipping post as well. Instead of asking why... 14 Jun 2010 04:06
Fallacy of missing subjunctive -- what's it called? What is the proper name of this fallacy? Statement: xxxx failed. A fallacy because without xxxx matters would have been much worse. I'll give a current example to illustrate its importance. The "stimulus bill failed. Unemployment is still high." But what if there had been no stimulus bill? (here is the ... 15 Jun 2010 15:25
*NEW DIGIT SEQUENCE* is an OXYMORON! This is proof of higher infinities! Take any list of real numbers digit expansions 123 456 789 DIAG = 159 ANTI-DIAG = 260 EVERYONE in sci.math thinks it's a NEW (NON COMPUTABLE EVEN!) digit sequence! EVERY digit sequence is computable up to ALL finite initial substrings. This means EVERY digit sequ... 14 Jun 2010 22:56 |