Logic

proof that once Finite is precisely defined that Algebra on infinite set is nonexistent #302; Correcting Math
I suppose that is a proof, of sorts, although I am not enamored by it. I want to prove that the only way to well-define or precisely define Finite is to pick a large number and say that is the end of Finite. But once that is accomplished the Infinity no longer has a mathematical Algebra because multiplication o... 23 Jan 2010 15:27

A rather very complex definition of Cardinality:
Hi all, I am still seeking a definition of Cardinality using the methodology of hereditarily sets that is supposed to work in ZF a lone (i.e without Choice). First we have the following as a theorem of ZF For every ordinal d Exist x For all y ( y e x <-> x is hereditarily strictly subnumerous to d ). x i... 15 Jan 2010 01:45

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Hi..how much for both? ... 15 Jan 2010 01:45

fantastic irony of mathematics-- well-define Infinity but loseout on multiplication and powerset and addition #296; Correcting Math
On Wed, 13 Jan 2010 19:09:07 -0800, Archimedes Plutonium wrote: [The usual ramblings.] For how many years have you been posting your junk now? 15? 20? Are you going to get a life any time soon? ... 14 Jan 2010 12:25

ZFC Can Prove Everything Provable? But how do you define "provable"here??
On 01/14/2010 02:17 PM, Andrew Usher wrote: The so-called standard model is supposed to include all the sets that "really" exist. Is this provable? If not, how is it not just blind faith? You have to start somewhere, yes. You have to make some basic assumptions about the "real" sets. These basic as... 14 Jan 2010 10:09

THE OTHERS ARE COMING
Pentcho Valev wrote: http://www.nybooks.com/articles/20279 Lee Smolin: "It is also disappointing that none of the biographers mention the writings that lead John Stachel, the founding editor of the Einstein Papers project, to speak of "the other Einstein". These writings look beyond his struggles with th... 19 Jan 2010 23:39

Axiom of Regularity:
Hi all, Is the following axiom equivalent to the axiom of Regularity? Axiom: For all x ( For all y (y e TC(x) -> ~ y e TC(y)) & For all y (y e TC(x) -> 0 e TC(y)) ). were "TC" stands for "Transitive closure" defined in the standard manner, and "0" stands for the empty set. Mor... 12 Jan 2010 21:53

If you “chose” to not consume you'd cease to exist !
On Jan 9, 10:01 pm, Gro...(a)JeffRelf.F-M.FM wrote: Anything that consumes is “alive”, I say. There are no “choices”, not really. If you “chose” to not consume you'd cease to exist ! Even the cosmos consumes; i.e. net net, entropy goes up as exergy/fuel is lost forever. I suggest laying off the quotes for a while. ... 10 Jan 2010 02:07

I was wildly too overoptimistic of proving Riemann Hypothesis when math range of validity is 10^500 #289 Correcting Math
Archimedes Plutonium wrote: (snipped) Now that also sheds light onto a bigger and major question. Once we confine all of Mathematics to the Planck Unit of 10^500 and its inverse, then the proof of conjectures such as Riemann Hypothesis take less than a day for a supercomputer to reveal that... 9 Jan 2010 22:54

finite ellipsis, and the Incognitum and Infinite ellipsis #287 mathematics ends at about 10^500
I already said that the two-dot ellipsis was reserved for Finite numbers where the definition of Finite is 10^500 and below (ditto for inverse). Now can I well-define the Incognitum? This is a little ways beyond the Finite realm and although we would never see this in Physics because a number such as 10^-500 K... 9 Jan 2010 16:18