Talk:Plus and minus signs/Archive 1

Pre-page-move
Perhaps there should be an ambiguity page set for 'plus'. This page references the PLUS ATM network, but there is also the PLUS! micorsoft productivity pack, and PLUS government funded student loans. [unsigned]

A question on terminology
I am a native Dane, but teach math in English at highschool level. I have a problem with terminology.

In Danish, "-5" and "-x" are read aloud as "minus fem" and "minus x", not "negativ fem" and "negativ x". How's that in English?

Many students would read "-5" as "negative 5", but that's nonsense to me as 5 is not negative. I.e., I understand "negative as a property, and 5 does not have that property. Am I right?

Also, many students would read "-x" as "negative x", but again, I'd understand that as "a negaitve x" (i.e. x<0), and that's of course something else. Am I right? Or am I at least right to the extent that "negative x" would be ambiguous?

I post this question at Talk:Negative and non-negative numbers too; please answer it there.--Niels Ø 14:06, 2 December 2006 (UTC)

(1+1 is 0) not binary
I wouldn't call the first (1+1=0) binary. "Binary" is a way to write symbols for the natural numbers $$\mathbb{N}$$. There, 1+1=2. Writing it binary as $$1+1=10_2$$ doesn't change the result, it's just two different symbols representing the same number. In contrast, $$\mathbb{F}_2$$ is a different thing. You can imagine $$1\in\mathbb{F}_2$$ as a 180 degree rotation. 1+1 would than mean rotating by 360 degrees. The result is the same as if the rotation didn't take place: That's $$0\in\mathbb{F}_2$$, and therefore 1+1=0, without any tricks like ignoring the overflow bit of an adder circuit. -- JeLuF 21:29 13 Jun 2003 (UTC)

Chinese joke
''A Chinese joke: What is "1+1"? Answer: &#29579; (wang).''

Eh? I don't get this. Is it just that the character can be made from the characters "1", "+", and "1" combined? If so, I don't see why it's funny... If this is a well-known joke among Chinese people, this fact needs to be explained in the article, and the joke itself should be explained. Otherwise, it should be removed. -- Oliver P. 22:44, 21 Aug 2003 (UTC)


 * I asked Wshun to explain the joke :-) Fantasy 08:14, 22 Aug 2003 (UTC)


 * It is a childish nonsense joke. If you answer 2, the correct answer is then &#29579;; if you answer &#29579;, the correct answer is then 2. So you could never be right :P BTW, I am surprised the joke can stay so long!!! Yes, it should be removed. --wshun 21:32, 22 Aug 2003 (UTC)


 * OK, maybe I have a too high esteem of Chinese wisdom, So that I think, there must be a sense, even if there is none... Sad, I was hoping for some humor in Wikipedia ;-) Fantasy 21:41, 22 Aug 2003 (UTC)


 * I kind of liked the joke. It is a harmless one, and somewhat opens up a window on Chinese culture/characters. Why not replacing it in the article with some explanation? After all, there are tons of articles about minor games in the 'pedia. olivier 11:18, 8 Sep 2003 (UTC)


 * Well, it's not exactly a joke but is more similar to a riddle or quiz from which a kid learns Chinese characters. Another example, what is 1 minus 1? Answer is &#19977; (literary meaning: three). kt&sup2; 01:02, 23 Nov 2003 (UTC)


 * Maybe we can have an article explaining these riddles of children. kt&sup2; 01:05, 23 Nov 2003 (UTC)

Plus and minus signs
There was something that approached a consensus for deletion; not quite, but one never knows what some over-eager admin will do as the deadline approaches. The closest thing to a consensus was to do something about reorganizing, renaming, whatever; so I up and did it. A better history of these notations is called for. Dandrake 00:54, Feb 28, 2004 (UTC)

VfD

 * One plus one not encyclopedic Anthony DiPierro 23:40, 21 Feb 2004 (UTC)
 * Keep, but maybe retitle, move, or merge with something else. Does have some interesting info. -- J. Antley 17:48, 21 Feb 2004 (CST)
 * Keep; agree with DarkFantasy. The contents are worthy of the encyclopedia, but wouldn't suffer if integrated somewhere. Dandrake 00:16, Feb 22, 2004 (UTC) See below.
 * Keep. It's a phrase that everyone use with a long and proud history. BL 10:43, Feb 22, 2004 (UTC)
 * Delete; this is inappropriately titled. Move/merge content to some article dealing with addition or uses of the plus sign. Psychonaut 14:05, 22 Feb 2004 (UTC)
 * Not addition; the entry shows clearly that this expression is not necessarily addition in any normal sense. And plus sign is a bit of a red herring: it's nothing but a redirect to addition&mdash;which reduces the problem to the previous case. Dandrake 04:56, Feb 23, 2004 (UTC)
 * Then change plus sign from a redirect to a disambiguation page which points to the various usages referenced in the one plus one article: addition, concatenation, etc. &mdash;Psychonaut 09:54, 23 Feb 2004 (UTC)
 * Delete. Pointless here. Everyking 20:42, 22 Feb 2004 (UTC)
 * Delete. We will have n-squared combinations otherwise.  I agree with suggestion for the info going into the pages for one and plus.  And binary etc.  No need for the collection of the info in one place.  Paul Beardsell 10:46, 23 Feb 2004 (UTC)
 * Delete - Texture 00:07, 24 Feb 2004 (UTC)
 * Bowing to the near-consensus, I've moved it to Plus and minus signs, which is more general than plus sign and suggests possible expansion to a collection of data on other familiar notations. The article needs a lot of work, which I'm beginning now. Dandrake 00:39, Feb 28, 2004 (UTC)

Trivia
I'd just like everyone to know that the technical name for a plus sign is a quadrapoint. -Bannus 11:09, 16 May 2006 (UTC)
 * That tidbit shows up on a few blogs, but it appears to be a hoax. I've removed it from the article. Melchoir 23:16, 26 June 2006 (UTC)

Removed section "Symbols used to code computations"

 * Computations require the hyphen-minus. Sometimes the sign of a negative number constant (i.e., part of the notation of the number itself) is written "¯" while the unary and binary minus operator is the hyphen-minus "-".

I removed the above section on the following grounds:
 * Computations require the hyphen-minus. Even if we infer the missing context (i.e. computations, as entered into a textual interpreter on a computer, typically use the hyphen-minus character as a minus sign), this is a woeful way of stating this. Computations only require the hyphen-minus in this way because historically that was the minus sign that computers offered. This historical background is sufficiently treated elsewhere in the article. (Edit: Or, it used to be&hellip;)
 * This is a fact about the present. I corrected a serious omission by adding it. It is weird if the article does not even mention how a subtraction is coded on a computer.--Patrick 06:07, 15 May 2007 (UTC)
 * But there's the same problem again! 'How subtraction is coded on a computer'&hellip; there is no one way to 'code subtraction'. It depends entirely on what you're talking about. Are you talking about source code for high-level languages? Yes, most of them use the hyphen-minus as the subtraction operator, because historically that was the minus sign, so it's what's present on standard keyboards. But what about the assembly code into which that source is compiled? There, subtraction is coded as a mnemonic like SUB or something. Or encoding in text? There, you can use the hyphen-minus, or you can (and should) use the true Unicode minus. You see? Context is everything. 'On a computer' is just not accurate. -- Perey 14:57, 17 May 2007 (UTC)


 * Sometimes the sign of&hellip; I have never encountered the practice referred to in the second part; the link goes to a PDF about the A+ programming language. Actually the very pressures of history that "require" the hyphen-minus make this a pretty esoteric thing to do, since the overbar isn't ASCII. (I see now from the A+ article that it does indeed need its own character set!)
 * It is not a recommendation, it is an interesting encyclopedic fact.--Patrick 06:07, 15 May 2007 (UTC)
 * You would still need to specify the context. 'Sometimes' is not enough; the correct context is 'In the A+ language' (and in any others that do the same). And then people would be free to debate whether this interesting fact (and I agree it's interesting) is notable enough for inclusion. -- Perey 14:57, 17 May 2007 (UTC)

A lot more explanation and context is required to make sense of this section, if it's possible to do; in the meantime, it's just confusing to have it in the article. -- Perey 18:26, 14 May 2007 (UTC)

Alternative plus sign
The section "alternative plus sign" makes curious statements with no citations. The section in its entirety has no purpose other than to defame the Jewish people. I feel it should be removed.


 * I don't see any defamation here. Either it's correct, or it's not. We could put an unsourced tag on it (and ultimately remove it) if it's disputed; otherwise, what's the problem?--Niels Ø (noe) 10:22, 12 July 2007 (UTC)

I will make my complaint more clearly. The statement:

The usual explanation for the practice is that it avoids the writing of a symbol "+" that looks like a Christian cross.

ought to be cited immediately, or removed. This sentence implies that Jews have a negative attitude toward the cross and its symbolism, which is certainly false. There is no way to assert the validity of the statement and is not relevant to the rest of the section. Other than this, there is no problem with the section. However, I should note that I attended orthodox Jewish schools from the elementary to high school level, and never once saw an "alternative plus sign" as described in the article.

I have removed the following from the article:
 * ==Alternative plus sign==


 * A Jewish tradition dating at least from the 19th century is to write plus using a symbol like an inverted T. This practice was adopted into Israeli schools (this practice goes back to at least the 1950s) and is now commonplace in most elementary schools (including secular schools) and some secondary schools. It is also used occasionally in books by religious authors, but most books for adults use the international symbol "+". The usual explanation for the practice is that it avoids the writing of a symbol "+" that looks like a Christian cross. Unicode has this symbol at position U+FB29 "Hebrew letter alternative plus sign" (﬩).


 * However - even if this may have been the case in the 50's in Israel - no religious attributes were added to this way of writing. Today it is definitely NOT common practice in elementary schools throughout the country.

The last paragraph was recently inserted; in addition to being misplaced, it contradicts the first paragraph. My edit summary was: Moving Israel-stuff to talk page, till sources have been found and concensus reached.--Niels Ø (noe) 10:40, 2 October 2007 (UTC)


 * Ah, so this is why someone tried to delete that section a few days ago.
 * A quick Google books search reveals an anecdotal account in The Holocaust in Three Generations that attests to the use of the alternative plus sign in Jewish schools in early 1940s British Palestine. Another source speaks of the alternative plus sign purely in the past tense, but it's Modern Templar, so I don't know how reliable that would be considered here. Certainly these sources don't cover the claims made in the old text.
 * For reference, the material was introduced in this edit. Melchoir 15:13, 2 October 2007 (UTC)

This should be mentioned in the article. The only dispute seems to be about its prevalence, not its existence (which is well-attested — after all, it's even in Unicode). We can just say that it has some (largely historical) use, without making any specific claims until we have better documentation.--Pharos 05:50, 15 November 2007 (UTC)
 * I've readded the paragraph per discussion above, with several references (including the one you menioned above) and using less absolute terms on the validitly of its prevalence today. I can say personally, which is not a WP:RS of course, that it is still used in some elementary schools (in the younger grades) in Israel today, though I'm not sure how many. Epson291 (talk) 06:10, 27 November 2007 (UTC)

Could someone explain this?
Meaning #3 of the minus sign:


 * "The opposite operator: A unary operator that takes the opposite (the additive inverse) of any quantity, as in −x."

Does this make any sense? What's it trying to say that's different from meaning #2? Could someone who understands it explain it more clearly in the article? Matt 14:13, 6 November 2007 (UTC).


 * Let me explain it here, and you let me know if it needs more explanation in the article. In meaning #2, the sign "-" is part of a numeral, specifically part of a negative numeral.  The numeral for "negative three" is "-3". In meaning #3, the sign "-" is a unary operator, that is, the operator that changes positive three to negative three.  An "operator" is a kind of function, a "unary operator" a function with one input.  Thus we can think of "-x" as the output of the function f(x) = -x.  As part of a numeral, "-" is always part of a numeral representing a negative number.  But -x may be negative, positive, or zero.  If x = -3, then -x = 3. Rick Norwood 15:34, 6 November 2007 (UTC)


 * Hi Rick, thanks for your reply. I do not see how the two uses can actually be distinguished. They are written identically and have identical meanings. For example, if you see "&minus;3" then how do you know whether it's intended to mean "numeral negative 3" or "unary minus operator applied to numeral 3"? I also think that the word "opposite" needs more explanation. I wonder why it doesn't just say "negative"? Is the idea to cover "normal negative" and analogous meanings in one hit? I think it would be clearer to kick off by saying &minus;x is the negative of x, and then add that it can be extended to analogous concepts, with some examples if possible. If that's what's intended. Matt 18:46, 6 November 2007 (UTC). —Preceding unsigned comment added by 86.133.242.214 (talk)

Two comments.

First, the reason to say "opposite" rather than "negative" is that -x may not be negative. You are correct that the symbology does not distinguish between the two meanings, just as the symbology does not tell you if 7 - 4 means "seven minus four" or "seven plus negative four". The symbols have been designed this way because the answer is the same in either case. The meaning really is different. Seven minus four means seven take away four, means seven, six, five, four, three. Seven plus negative four means split seven into two parts, 3 and 4. Have the negative four cancel out the positive four (since they are opposites), leaving three. Same answer, different meaning, identical symbols.

Second, while in the United States our public school system is so poor that most students never learn that a negative sign represents an opposite, that is in fact what it represents, and articles on mathematics should say so, even if American textbooks do not. If + represents up, - represents down, if + represents a deposit, - represents a withdrawal, and so on.

Rick Norwood 13:38, 7 November 2007 (UTC)


 * I'm not talking about binary expressions such as 7 - 4, I'm talking about the distinction between the supposed two meanings of, for example, "-5". Once "-5" is defined it can be used in expressions like any other number; that is a separate matter. Incidentally, you are wrong that the symbology does not tell you if 7 - 4 means "seven minus four" or "seven plus negative four". "7 - 4" definitely does not mean "seven plus negative four; this is written as "7 + (-4)". "Seven minus four" and "seven plus negative four" are, as you rightly say, conceptually different things that happen to give the same answer, and the different notation indicates that. The same does not apply to "-5" by itself: there is conceptually only one thing here.


 * The unary minus operator returns the negative of its operand; it does this in exactly the same way irrespective of whether its operand is 5, 112.67 or x. This is not the same thing as saying it returns a negative number; I am well aware that -x is positive when x is negative. Anyway, the current wording really is IMO very confusing, so I have made some changes. I have never heard of unary minus being called the "opposite operator", and a Google search doesn't convince me that this is a common term, so I removed it. Please reinstate if you are confident that this term is in common use. It could be a US/UK thing I suppose. Matt 02:05, 8 November 2007 (UTC).

If one were bending over backwards, one might write 7 + (-4); in practice, one almost always writes 7 - 4.

No, - 5 really does have two uses. If I'm labeling ticks on the left axis, - 5 is pure number. In the statement, if f(x) = -x then f(5) = -5, I'm applying a unary operator to 5.

No, the unary operator commonly called minus does NOT return the negative of its operand. A number is negative if and only if it is less than 0.

What we have here is one of those situations where there is a common language and a careful language. Situations like this one confuse students, but the common language is strongly resistant to change. Yet another example, dy/dx should be read "dy over dx" but is always read "dy dx". That doesn't mean that we multiply!

So, I am not saying that unary minus isn't commonly called "negative", I'm saying that what it is commonly called is technically wrong, and that until students gain a certain amount of mathematical sophistication, it is better to tell them what is correct, and then tell them what is customary.

Rick Norwood 18:33, 8 November 2007 (UTC)