# Mathematical Writing Style Questions

I think Math.SE may not be the right venue for a simple question I have:

In English, is there any difference between: for all $c>0$ and for any $c>0$ ? I think the later sounds better but not sure. In terms of style, what would be preferable?

If Math.SE is not the right venue for style questions. Is there a good place? I know there is an English site but there it is less likely it will get the attention of professional mathematicians or related.

• Personally, I think that this is a good question for the main site. There is, after all, a terminology tag. – user1729 May 14 '14 at 14:32
• (Also, to answer your question, I think that "for all" is better simply because it is standard. If you use "for all" then I know precisely what you mean, while if you use "for any" then I will have to first convince myself that what you actually mean is "for all" and go from there...) – user1729 May 14 '14 at 14:34

It is true that questions like this are often closed as "primarily opinion-based", but personally I would find this a good question for the main site, if it were asked well. In particular:

• Consider using the following tags: , , .

• As much as is possible, phrase your question in a way that makes it less a matter of opinion and more a matter of fact.

• Keep things in the scope of mathematics and proof-writing. Don't ask what these phrases mean in English, but rather ask what they mean in mathematical writing, and which to use when in your own mathematical work.

• Include clear examples of where you feel there may be some ambiguity or why you are concerned about the difference between these phrases.

Don't feel too bad if your question is closed anyway, because sometimes that's the way things go. But I think it is quite possible your question will be well-received.

No, I don't think questions like 'which expression sounds better' is on-topic on Math.SE. (It's not a mathematical question, and on top of that most style questions are subjective.)

Not sure about a good place for such questions. You can ask it in chat, of course...

• P.S. As for the question itself, Halmos (in «How to write Mathematics») writes: $$\,$$ The point is that in everyday English «any» is an ambiguous word; depending on context it may hint at an existential quantifier («have you any wool?», «if anyone can do it, he can») or a universal one («any number can play»). Conclusion: never use «any» in mathematical writing. Replace it by «each» or «every», or recast the whole sentence. – Grigory M May 14 '14 at 14:46