Talk:Boolean values: Difference between revisions
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:::::: Quoting that page: ''There are at least four different and incompatible systems of notation for Boolean rings and algebras. ... The old terminology was to use ... "Boolean algebra" to mean a Boolean ring with an identity.'' --[[User:Rdm|Rdm]] 20:03, 1 May 2012 (UTC)
::::::: Yes, and read on: ''Also note that, when a Boolean ring has an identity, then a complement operation becomes definable on it'' --[[User:Ledrug|Ledrug]] 20:06, 1 May 2012 (UTC)
:::::::: Except: that statement is provably false. Consider the ring I have been using as an example: LCM has the identity value 1. GCD has the identity value 0. But no complement can exist except in the two-valued case. --[[User:Rdm|Rdm]] 20:21, 1 May 2012 (UTC)
::: 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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