Talk:Boolean values: Difference between revisions
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:: 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) |
:: 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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::: Eh I didn't say anything about two-valued system. Go through literatures and you'll see that LCM and GCD can make a Boolean algebra on ''some'' bounded sets like {1, 2, 3, 6} (all divisors of 6); on the set of all positive integers (or non-negative integers, or all integers) it doesn't work because you can't have a consistent complement/NOT operator, as I've shown above. You can forgo the NOT operator and universal bounds, and call the rest "Rdm Algebra", or "Ledrug Algebra" if you don't like it, but it's not Boolean: Boole intended to formalize thought process and decision making, thus lacking a negation operation makes it singly useless in this regard. |
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::: As to Shannon "dumbing it down" (I guess you'd rather put it this way) to two values, again, since it's about decisions, making the results always "yes" or "no" is at least practical. |
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::: More to the point of the task, though, is that I think the task is fine as is; within the context of computers, it's not wrong to think "Boolean values" means "true or false". If you want to introduce another task on Boolean algebra in the more formal mathematical sense, that's fine too, just make sure your introductory example is correct. --[[User:Ledrug|Ledrug]] 17:45, 1 May 2012 (UTC) |
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