only in practice
On Sat, Apr 20, 2013 at 8:23 PM, John Carlson <[email protected]> wrote: > Take my word for it, theory comes down to Monday Night Football on ESPN. > On Apr 20, 2013 10:13 PM, "John Carlson" <[email protected]> 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" <[email protected]> wrote: >> >>> On 4/20/13, John Carlson <[email protected]> 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 >>> [email protected] >>> http://vpri.org/mailman/listinfo/fonc >>> >> > _______________________________________________ > fonc mailing list > [email protected] > http://vpri.org/mailman/listinfo/fonc > >
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