Take my word for it, theory comes down to Monday Night Football on ESPN. On Apr 20, 2013 10:13 PM, "John Carlson" <yottz...@gmail.com> wrote:
> I think that concepts in some sense transcend the universe. Are there > more digits in pi than there are atoms in the universe? I guess we are > asking if there are transcendental volumes which are bigger or more complex > than the universe. If the universe contains the transcendental as symbols > then how many transcendental symbols are there? I think you still run into > Russell's Paradox. > On Apr 20, 2013 9:15 PM, "Simon Forman" <forman.si...@gmail.com> wrote: > >> On 4/20/13, John Carlson <yottz...@gmail.com> wrote: >> > Do you need one symbol for the number infinity and another for denoting >> > that a set is inifinite? Or do you just reason about the size of the >> set? >> > Is there a difference between a set that is countably infinite and one >> that >> > isn't countable? I barely know Russell's paradox... you're ahead of me. >> >> Well, for what it's worth, quoting from Meguire's 2007 "Boundary >> Algebra: A Simple Notation for Boolean Algebra and the Truth >> Functors": >> >> "Let U be the universal set, a,b∈U, and ∅ be the null set. Then the >> columns headed by “Sets” show how the algebra of sets and the pa are >> equivalent. >> >> Table 4-2. The 10 Nontrivial Binary Connectives (Functors). >> >> Name Logic Sets BA >> >> Alternation a∨b a∪b ab >> Conditional a→b a⊆b (a)b >> Converse a←b a⊇b a(b) >> Conjunction a∧b a∩b ((a)(b)) >> ___ >> NOR a↓b a∪b (ab) >> ___ >> Sheffer stroke a|b a∩b (a)(b) >> >> Biconditional a↔b a⊆b⊆a (((a)b)(a(b))) -or- ((a)(b))(ab) >> >> (Apologies if the Unicode characters got mangled!) >> >> Check out http://www.markability.net/sets.htm also. >> >> >> I don't know much about set theory but I think the "Universal" set >> stands for the set of everything, no? >> >> Cheers, >> ~Simon >> >> >> >> >> >> "The history of mankind for the last four centuries is rather like that of >> an imprisoned sleeper, stirring clumsily and uneasily while the prison >> that >> restrains and shelters him catches fire, not waking but incorporating the >> crackling and warmth of the fire with ancient and incongruous dreams, than >> like that of a man consciously awake to danger and opportunity." >> --H. P. Wells, "A Short History of the World" >> _______________________________________________ >> fonc mailing list >> fonc@vpri.org >> http://vpri.org/mailman/listinfo/fonc >> >
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