# “denote XXX shortly by X” or “denote shortly XXX by X”

I think these two forms are correct:

• We will denote XXX shortly by X.
• We will denote shortly XXX by X.

However, I don't know which one is more natural.

• It's really hard to tell which is more natural when you use XXX and X. I really wish more people would write real sentences instead of using placeholders like that, particularly when asking about which is more natural. Sometimes, verbs and prepositions work better with some objects than others. – J.R. Mar 6 '18 at 11:55
• @J.R. I have done it in such a way because this kind of problems appear in mathematics where you abbriviate one long symbol with another shorter one. Let's say that XXX=A_{phi} and X=A. – Fallen Apart Mar 6 '18 at 12:20
• We will abbreviate or We will represent A_{phi} as A. – StoneyB on hiatus Mar 6 '18 at 12:23
• @StoneyB I would avoid word "represent", because it has some mathematical meaning sometimes. Does the word "denote" fit for such purpous or should I use "abbreviate"? However, it still does not answer my original question. – Fallen Apart Mar 6 '18 at 12:31
• I'm not sure shortly is the word you want at all. Shortly means something like "very soon", not "in a short way". – stangdon Mar 6 '18 at 12:49

If you're trying to say that X is a short form of XXX, then neither of your sentences expresses this clearly. "Denote shortly" just doesn't mean that in English, since the adverb "shortly" in English almost always applies to a period of time, not a physical size. Here is a proper use of "shortly":

Have a seat. Your waiter will be with you shortly. [i.e., very soon]

If you are establishing a short form of a term or variable, you could say it like this:

We will denote XXX with the short form X.

or

For the sake of brevity, XXX will be abbreviated as X.

• I would not use denote. "Let the short form X stand for XXX". – Lambie Mar 6 '18 at 16:45
• If the context is a mathematics paper, then "denote" meaning "represent symbolically" is common usage. If the context is other than formal mathematics (or a closely-related science like physics), then I agree that denote sounds stilted and overly-formal. – Canadian Yankee Mar 6 '18 at 17:01
• The common term used in math is stand for, not denote. It sounds out of context. This is not a semiology paper about math. – Lambie Mar 6 '18 at 17:04
• @Lambie How about: "we will denote the set of all fixed points by Fix"? Does it sound right to you? Or do you only claim that denoting one symbol by another does not fit. Btw., haven't you see the use of the word "shortly" in this context? I am certain that I did. Just google "denote shortly" and find out yourselves. – Fallen Apart Mar 6 '18 at 22:01
• @FallenApart I think you are misusing the word denote. Yes, I saw the use of shortly, it is wrong. Google does not have a mind regardless of what some may think. :) – Lambie Mar 6 '18 at 22:45