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Talk:Boolean values: Difference between revisions
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== two Pythons ? ==
Python twice?
:It's already been noted. a merge is in the works. --[[User:Mwn3d|Mwn3d]] 20:20, 10 July 2009 (UTC)
Sorry about the wait. All done. --[[User:Paddy3118|Paddy3118]] 21:12, 10 July 2009 (UTC)
== Rename page? ==
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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:
::::::::: Er, no: 0 is a lousy identity for GCD. What's GCD(0, 0)? --[[User:Ledrug|Ledrug]] 20:34, 1 May 2012 (UTC)
:::::::::: GCD maps to Logical OR, and LCM maps to Logical AND when 0 maps to false and 1 maps to true. GCD(0, 0) is AND(false, false). Note that we are defining LCM and GCD to satisfy the constraints of Boolean Algebra (in the sense of a Boolean Ring with Identity), and this drives the definition in the cases which would otherwise be undefined. --[[User:Rdm|Rdm]] 20:47, 1 May 2012 (UTC)
::::::::::: 1 doesn't work as indentity for GCD either: GCD(1, x) = 1, not x.
:::::::::::: Yes. Ouch. My last edit corrected a non error. I was in a hurry and not paying attention. Rewinding (and reverting part of my last edit). GCD(0, 0) must be 0, by definition based on the rules of Boolean Algebra. The point here is that we define GCD to satisfy the rules of the algebra. --[[User:Rdm|Rdm]] 21:19, 1 May 2012 (UTC)
::::::::::: Anyway, this is quickly growing into a pissing contest, and I should stop here. Let me just reiterate my position on this task: I think it's fine to keep the title as is, but it's reasonable to give a brief mention of the broader sense of the word "Boolean" if you feel like; if you want to make a new task about general Boolean algebra, make sure your example is waterproof. /zip my mouth on this subject now.--[[User:Ledrug|Ledrug]] 21:08, 1 May 2012 (UTC)
:::::::::::: Ok, I will think about creating a page for that task. Thanks. --[[User:Rdm|Rdm]] 21:19, 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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:::We do not have to rename the page -- that was just a suggestion -- but I think we do need to mention that we are using the redefined version of the term.
:::Note also that we do have tasks here which focus on mathematical issues. --[[User:Rdm|Rdm]] 19:54, 1 May 2012 (UTC)
:::: I reread the title and task description and took a look at the Wolfram article and the wp article and I think it would be difficult for someone to confuse the meaning of this page and what is required to solve it. If a mathematician is used to many valued logics then the fact that only two values are mentioned in the description should be enough to set them straight (although it would be odd that the mathematician not know that the two valued set is the default in most computer languages). I would go along with those that want to keep this description but who are not averse to seeing a task in other-valued Boolean logic. (Being obscure, this other task may need careful explanation). --[[User:Paddy3118|Paddy3118]] 12:11, 7 May 2012 (UTC)
::::: This is not about "many valued logics". If you want to deal with "many valued logics" you might be using a container which holds multiple logical values. Or, you might be using "fuzzy logic" where logical values are represented using a fractional value in the range [0..1] instead of a single bit.
::::: The confusion I am concerned with is the linguistic pressure to treat "Boolean" as equivalent to "Logical". That's a valid shorthand in the context of the two valued boolean algebra. But it loses track of what makes boolean algebra "boolean" in the first case.
::::: And this confusion happens a lot. Every time someone says "Integers are not Booleans" they are expressing this confusion. And that statement is distressingly common even among people with PhDs with a focus on type theory. --[[User:Rdm|Rdm]] 13:25, 7 May 2012 (UTC)
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