Talk:Logical NOR

message: The supposed proof is only a `proof' that such a single operator system is not necessarily incomplete, that is, it fails to satisfy a sufficient condition for incompleteness.
In short the argument establishes nothing of interest (towards the supposed aim of demonstrating functional completeness).
Pushing the negation in: "using only nor *might* be functionally complete" is what the mini-section actually makes an argument for.
The first principles method for a corrected argument would be an explicit construction of all 16 binary boolean functions as expressions using only "nor".
Of course it would suffice to demonstrate just the reduction of `and', `or', and any form of `not' (the obvious one being unary negation, but it suffices to to consider either of the binary forms that ignore either the first or second argument); any reader would already recognize, indeed, prefer, this definition of what makes a Boolean algebra complete.
Formally this looks like, perhaps going the extra mile to define false (i.e., as (false p) := (nor p (not p)), so that one truly needs just one logically constant symbol "nor"), in prefix notation:
  (not p) := (nor p p),
  (or p q) := (not (nor p q)), and finally
  (and p q) := (nor (not p) (not q)).
With strict formality the parentheses can be everywhere dropped, and so for example "(and p q)" expands to:
  nor nor p p nor q q.
A fully detailed proof then finishes by actually backing up the implicit claims of the definitions, say: "(true-not (nor p q))" is, by the definition of "nor", equivalent to "(true-or p q)"
ergo "(true-not (not p))" expands to "(true-or p p)" and hence "(true-not (not p)) = (true-identity p)".  It is an elementary property that true-not is its only inverse, 
therefore both "not = true-not" and "or=true-or" are shown.  Finally "and=true-and" follows by applying De Morgan's law.
So far as the article is concerned though merely the definitions should suffice, or at least, such
would go just as far as the current mini-section goes, but, in the `right' direction.
--
However the present section actually serves to point to far more advanced topics on formal results pertaining to abstract boolean algebras;
a truly correct edit must figure out the right way to phrase why the observation+reference is interesting rather than merely replacing the content with a correct argument towards the wrong goal.  — Preceding unsigned comment added by 72.223.117.66 (talk) 16:43, 7 March 2012 (UTC)
thread_title: proof of functional completeness

message: I have been working on all of the logical operators recently. I would like to see a consistent format for them. There is a wikiproject proposal for this at:
Wikipedia:WikiProject_Council/Proposals#Logical_Operators. Also see Talk:Logical connective.
I would like to see the logical, grammatical, mathematical, and computer science applications of all of the operators on the single page for each of those concepts. 
Gregbard 08:44, 28 June 2007 (UTC)
thread_title:  Proposed project 

message: "Ampheck" is listed under "see also" at the bottom of this "Logical NOR" page, but that link merely redirects back to the "Logical NOR" page.  Perhaps some mention of the term "Ampheck" should be included in the text.  I'd add it myself except I don't know what it means (which is why I clicked on it).
I agree this is confusing. --68.0.124.33 (talk) 07:40, 19 February 2008 (UTC)
replies: text: "Ampheck" once had its own article, started by a somewhat problematic editor. Apparently this is a term coined by Charles Peirce that can refer to NAND as well as to NOR. I don't think we have to cover all of Peirce's idiosyncracies here, so I just removed the word from the "see also" section. See also Jon Awbrey's ampheck article on PlanetMath. --Hans Adler (talk) 18:06, 19 February 2008 (UTC)
replies: text: Other articles link to "Ampheck", which redirects here. In that case one would expect to see at the very least a short history of the original term whose definition is sought. --Nekiko (talk) 22:29, 20 September 2012 (UTC)
thread_title: Ampheck

message: Why on Earth does a search for "pierce arrow" redirect to this page? -- 64.223.230.30 01:39, 25 May 2008 (UTC)
replies: text: I suppose you mean Peirce arrow. The redirect seems to be due to an obsolete(?) notation of NOR as an arrow pointing downwards. This should probably be added to the article, as a minor detail of notation. --Hans Adler (talk) 11:40, 25 May 2008 (UTC)

text: Someone fixed the problem. --Hans Adler (talk) 22:51, 23 November 2008 (UTC)
thread_title: Er, what?

message: I noticed that the material conditional is written to be equivalent to NOR as:
p → q ≡ ((p NOR q) NOR q) NOR ((p NOR q) NOR q)
However, when I tried to verify this with a truth table, I determined that the truth value of this equivalence does not match that of the material conditional, but a switching of the last p with the q in the both the left and right terms fixes this:
p	q	(p NOR q)	(p NOR q) NOR p	((p NOR q) NOR p) NOR ((p NOR q) NOR p)	p → q
T	T	F        	F              	T                                      	T
T	F	F        	F              	T                                      	F
F	T	F        	T              	F                                      	T
F	F	T        	F              	T                                      	T
p	q	(p NOR p)	(p NOR p) NOR q	((p NOR p) NOR q) NOR ((p NOR p) NOR q)	p → q
T	T	F        	F              	T                                      	T
T	F	F        	T              	F                                      	F
F	T	T        	F              	T                                      	T
F	F	T        	F              	T                                      	T
Have I made a mistake, or is this article's equivalence incorrect?  If I am wrong, where did I err in my table?
--BBUCommander (talk) 02:34, 8 July 2009 (UTC)
replies: text: I agree with your table as well as with your proof. Good catch. Remember kids: don't blindly trust Wikipedia when you write your cheat sheets. Adrianwn (talk) 19:52, 1 August 2009 (UTC)
thread_title:  NOR and Material Conditional