Talk:−1

message: Isn't the action of "raising a number to the power of -1" defined as "the same thing as calculating its reciprocal"? Dysprosia 09:35, 10 Feb 2004 (UTC)
replies: text: I guess the way I expressed it was inelegant. Can you reword it more elegantly? PrimeFan 20:36, 10 Feb 2004 (UTC)
replies: text:  It's not that, it's just I'm usually wrong on matters such as this - but things are changing! I think I'm right, though, so if I'm wrong, then the correcty-person can change the article :) Dysprosia 23:48, 10 Feb 2004 (UTC)
replies: text: You are correct, and you have made the article more elegant. Your addition on the rules of exponentiations is much appreciated. PrimeFan 18:36, 11 Feb 2004 (UTC)
thread_title: Definition of reciprocal

message: Using a sufficiently broad meaning of 'definition', almost anything can be defined as almost anything; bearing that in mind, can anyone provide a source where, in mainstream mathematics, -1 was defined as the "square of i", without the imaginary units first being defined in terms of their relationship to -1? I seriously do not see it happening.
Although admittedly not having read the whole of the preceding discussion, I must object to the encyclopedic relevance of the Möbius function in its present context. Maybe if we created a "Uses of -1 in Mathematics" section, and listed e^i*pi, Möbius, Legendre symbol etc. Right now the intro has no cohesion. Pietro KC 07:04, 11 February 2006 (UTC)
thread_title: Beginning of article

message: I like your intuitive explanation, but I wonder whether material like
What would it mean to lay down a stick "negatively many times"? One answer is to say that it would result in a displacement where, if we were to lay it down 3 times immediately after, we would return to where we started.
will be clear to the beginning reader. (To be sure, I don't know; I'm not one, and I don't have one handy.)  So I'd like to propose an alternative intuitive explanation for your consideration.  It would read something like this:
Imagine, for a moment, that you're in a hot-air balloon. You have the flame going, so your balloon is rising. Let's say that you're rising at a nice steady climb: 2 feet every second. Let's also say that we'll consider up to be a "positive" direction, and down to be a "negative" direction.
Question 1: compared to where you are now, where will you be in 5 seconds?
Answer: you multiply the number of seconds by the speed. (5 seconds from now)(2 feet higher every second) = 10 feet higher. 5 x 2 = 10 -- a positive result.
Question 2: compared to where you are now, where were you 5 seconds ago?
Answer 2: let's think of time in the past as a "negative time" direction. (5 seconds ago)(2 feet higher every second) = 10 feet lower. (-5) x 2 = -10.
Now, let's change the situation. The flame isn't on, and in fact there's a small hole in the balloon, so you're slowly dropping -- 2 feet every second.
Question 3: compared to where you are now, where will you be in 5 seconds?
Answer 3: (5 seconds from now)(2 feet lower every second) = 10 feet lower. 5 x (-2) = -10 -- a negative result.
Question 4: compared to where you are now, where were you 5 seconds ago?
Answer 4: (5 seconds ago)(2 feet lower every second) = 10 feet higher. (-5) x (-2) = +10. A negative times a negative came out to be a positive.
Your thoughts? --Jay (Histrion) (talk • contribs) 16:05, 27 September 2006 (UTC)
replies: text: I like it!--155.144.251.120 00:41, 21 February 2007 (UTC)

text: I also think it is a much more intuitive example than is currently in the article as it uses an example in 2 dimensions to explain a 2 dimensional problem. I think it needs to go in ASAP so im going to get rid of the old one. If anyone really disagrees then revert the page. JackSlash (talk) 00:59, 24 March 2008 (UTC)
thread_title: Another intuitive explanation?

message: -1's relation to abelian groups, fields, and set theory should be mentioned.  Also the question posed in the article is completely inappropriate. I might change it myself in a little while but I think the writer of the article would be better qualified.--Cronholm144 21:54, 12 May 2007 (UTC)
thread_title: consider mentioning set theory

message: Short problem with the wording of this article. The word "negative" is an adjective. It means "less than zero." The term "negative one" has no meaning. The number "one" is a positive number, it is greater than zero.. there is no other number "one" which is also less than zero. The correct terminology here should be "minus one." Ratches (talk) 20:15, 5 May 2008 (UTC)
thread_title: Minus One vs Negative One

message: People often get stuck on one definition of a word, maybe the way they learned it or have heard it. Other people have used other definitions. All my life, in school, USA, Lousiana and Arizona, I have heard the term "negative one", so I think in actual use it is synonymous with "minus one". — Preceding unsigned comment added by 68.3.245.178  (talk • contribs) 15:42, 8 November 2012
I came here in search for an answer to this very question: Where does the term "negative one" come from? 
I've been working in mathematics and physics research and teaching for 25+ years both in English and non-English speaking countries, and my research activity has always been "in English". 
I never heard that term until I started to watch YT videos on mathematics and physics a few of years ago. 
I asked this question in the comment sections of many of those videos, but I never got an answer. 
Maybe I get one here (in a few years?). 
My theory is: It is a term introduced (invented?) by American school teachers (or actually those that teach math teaching) based on the "idea" that there is a difference between "–5" and "4–2", and therefore those operations should have different names. What confirms my theory is that there is also a certain type of calculators that also make this distinction, i.e. different keys for the unary and the binary "–", and these calculators are always those that are made for schools.  
And by the way, no, "negative" and "minus" are not synonymous. As far as I have noticed, those who call "–6" "negative six", do not read "–x" as "negative x", for the obvious reason that in general it isn't negative, so it would be misleading and confusing. However, the meaning of the unary operator "–" in "–x" is exactly the same as in "–6", so obviously the terminology used by the "negative one" scholars is also inconsistent. Hjm (talk) 21:46, 29 November 2019 (UTC)
thread_title: "Negative" is synonimous with "minus"

message: Dear Colleagues,
There is an ongoing discussion on the organization of number pages and number disambiguation pages.
Your comments would be much appreciated!! Please see and participate in:
* Wikipedia_talk:WikiProject_Numbers#Organization_of_number_pages
Thank you for your participation!
Cheers,
PolarYukon (talk) 15:42, 8 January 2010 (UTC)
thread_title: Organization of number pages and number disambiguation pages