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"
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