Talk:Boolean values: Difference between revisions
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:* 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)
:: GCD and LCM work just fine as boolean operators if the set you are dealing with is non-negative integers. Using the set of integers can also work with a minor clarification about the sign of least common multiple (for example: the result of lcm has the same sign as the product of the two numbers).
:: But it was Shannon that placed the emphasis on restricting focus in boolean algebra to the two-valued case. Boolean algebra on integers was established well before this. And, nowadays, because so many people have been working with computer languages which use "boolean" as a synonym for "two valued boolean", we are losing track of what boolean algebra is. The reference works (such as the ones I cited) focus almost exclusively on the "logic value" case, but shy away from the issue of what distinguishes "logic" from "boolean algebra". --[[User:Rdm|Rdm]] 13:06, 1 May 2012 (UTC)
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