Talk:Boole's expansion theorem

Names

Two articles with similar names, both quite confusingly written for new readers. Would be good to expand them with examples/combine into one. I would, but came here looking for info on Shannon, so I'll update it when I've figured out what to write. Bwgames 15:13, 22 January 2006 (UTC)

I've added info based on a copy of Shannon's 1948 seminal paper that I have with me. Help appreciated with further editing (including cleaning the example and merging in the page "Shannon's expansion theorem", which is misnamed - this is not a theorem). 213.58.128.215 13:38, 19 July 2007 (UTC) A.B.Leal

Copyright and Merger Fixed

I merged the files together but can't delete the other one - the other one was kind of copyrighted but now that has been resolved - I fixed the mess. Hope it makes a lot of sense now! LOTRrules (talk) 14:50, 27 January 2008 (UTC)

Citation

Does anyone has a "real" citation for the proof of Bool? I would be glad if one could add one or -- if not -- change the sentence into smth like "is normally attributed to George Boole". thanks —Preceding unsigned comment added by 147.210.129.49 (talk) 13:58, 5 February 2008 (UTC)

This article had been copied from another webpage

This article was copied from this page when it was merged with Shannon's expansion theorem in 2008, the later one being a pure copy of the external page, so I put back the article before the merge. Freewol (talk) 14:27, 8 April 2013 (UTC)

Improvements

This article needs work to be intelligible to beginners. Consider replacing the lede paragraph with this, if it's correct:

Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity

$F=x\cdot F_{x}+x'\cdot F_{x}'$,

where $F$ is any Boolean function, $x'$ denotes the complement (negation) of $x$, and $F_{x}$and $F_{x}'$ are $F$ with the argument $x$ equal to $1$ and to $0$ respectively.

I also think more needs to be said about $x$ being a vector of Boolean values. Jess (talk) 21:06, 14 July 2016 (UTC)

Take a look at my edit. x is not a vector of Boolean values, but a Boolean-valued variable. --Macrakis (talk) 22:00, 14 July 2016 (UTC)

Symbols

The use of "$\cdot$" and "$+$" for Boolean operators has long been deprecated. The article would be easier to understand if "$\cdot$" and "$+$" were replaced by "$\wedge$" and "$\vee$", or by "&" and "|", or even just by "AND" and "OR". Also replace "$x'$" by "$\neg x$".108.234.224.230 (talk) 00:31, 7 September 2018 (UTC)

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Proof

Can someone help flesh out the claim that "[the] Proof for the statement follows from direct use of mathematical induction, from the observation that $f(X_{1})=X_{1}.f(1)+X_{1}'.f(0)$ and expanding a 2-ary and n-ary Boolean functions identically." The base case for 1 variable is self evident, but the casual mention of expansion of 2-ary and n-ary functions seems unfounded. What am I missing? EulerPie (talk) 23:43, 25 September 2017 (UTC)