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I am unsure which is the right spelling (if there even is a ‘right’ spelling), but maybe native speakers can enlighten me: When should I use

  • fixed point
  • fixed-point
  • fixedpoint

when I refer to the point itself, but also in composite works (“fixed point equation”, “fixed-point juggling”, “fixed-point operator”)?

And do the same rules apply to prefixed points?

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When it is a phrasal adjective you use a hyphen. So when it modifies a noun uses a hyphen: fixed−point equation, fixed−point operator, fixed−point theory. But, on the other hand, take a fixed point of the operator, consider the fixed point in $X$. We have found our fixed point. When the phrasal adjective ends with -ly, drop the hyphen, the -ly is your separator. So perfectly separated set... Fixedpoint is ugly (never use it). –  Rabee Tourky May 22 '13 at 9:44
    
Thanks! Could you turn that into an answer, as I’d like to accept it? –  Joachim Breitner May 22 '13 at 10:42
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The underlying rule here is that you only need to hyphenate noun phrases that are being used adjectivally. Not doing so can lead to confusion - does the phrase 'fixed point theory' refer to a theory of fixed points or a fixed theory of points? –  HJRW May 22 '13 at 14:21
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2 Answers

up vote 12 down vote accepted

When it is a phrasal adjective you use a hyphen.

So when it modifies a noun uses a hyphen: fixed−point equation, fixed−point operator, fixed-point theory.

But, on the other hand, take a fixed point of the operator, consider the fixed point in X. We have found our fixed point.

When the phrasal adjective ends with -ly, drop the hyphen, the -ly is your separator. So perfectly separated set

... Fixedpoint is ugly (never use it).

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Except that you should really do as you say and use a hyphen (fixed-point, U+002D, TeX: -), not a minus sign (fixed−point, U+2212, TeX: dollar-dollar). –  Emil Jeřábek May 22 '13 at 11:45
    
So the answer originally began as follows. If $(F_1,F_2)$ is an ordered pair modifying the noun $N$, then we write $F_1-F_2$ $N$. But then I thought that was being too cute, so I cut and pasted... –  Rabee Tourky May 22 '13 at 13:09
    
This is exactly right. Even native speakers get it wrong all too often. –  Lubin May 22 '13 at 13:19
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@Lubin There's no such thing as right or wrong in language. If you feel native speakers get something "wrong" too often, it's either that a significant minority speaks/writes in a way you don't like or that it's your language use that is different from the norm. This is how descriptive grammar works. Of course, if you're talking about a specific "style," there is the right way. But then, whether the writer is a native speaker doesn't matter. Anyone can adopt any standard style. –  Yuichiro Fujiwara May 22 '13 at 14:41
    
As noted above, this is very nearly correct but not quite. (Acknowledging Yuichiro's objections, let me modify that as follows: this advice will lead to unnecessary hyphenation in certain cases, and many writers regard hyphenation as ugly and to be used sparingly.) Ambiguity is only a problem when the adjectival phrase is a noun phrase; if it isn't, the hyphenation shouldn't be necessary. The '-ly' exception is trying to get at this, but is really just an ugly hack that doesn't quite get at the underlying point. 'Well tempered clavier' is a nice example. –  HJRW May 23 '13 at 11:05
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All three are acceptable. Your list is in the order of preference. For hyphenated words, the important thing is to be consistant throughout the document. Prefix is a noun and you would not use past tense.

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"prefixed" here most likely comes from "pre-fixed", not "prefix+ed". I guess this shows once more the importance of using hyphens. :) –  Federico Poloni May 22 '13 at 11:34
    
Google shows both “prefix point” and “pre-fixed point” – which one is the right one for the x in $f x \le x$? –  Joachim Breitner May 22 '13 at 12:09
    
I am not familiar with that definition --- I call pre-fixed point a point $x$ such that $f(x)\neq x$, but $f^k(x)=f^{k+1}(x)$ for some $k\geq 1$. –  Federico Poloni May 22 '13 at 18:49
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