Anonymous user
Talk:Boolean values: Difference between revisions
→Rename page?: better example?
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Also, I cannot find any treatment of "logical not" in older treatments of boolean algebra. It has been added to newer works, but in that context it seems to be an arbitrary operation (it might be 1-x, or it might be any of a wide variety of other operations).
: Using the Mathworld page you cited, which LCM as "and", and GCD as "or":
:* Eqs. 1-8 are sastified;
:* For eqs. 9-12, we have LCM(a, Ø) = Ø and GCD(a, Ø) = a for all a; only viable candidate for Ø is Ø = 0. Similarly, LCM(a, I) = a and GCD(a, I) = I means I = 1.
:* for (13), LCM(a, ¬a) = Ø = 0, given any finite non-zero a, ¬a has to be 0; but this leads to a problem in (14): now GCD(a, ¬a) = GCD(a, 0) = a, not I.
: It would seem plain GCD and LCM don't make good Boolean operators. You'd have to map numbers to sets to have a viable definition. --[[User:Ledrug|Ledrug]] 22:54, 30 April 2012 (UTC)
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