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I want to write in math mode that something is compared to something else. It is, I want to say that both quantities have the same order of magnitude. What symbol should I use?

\documentclass{article}
\begin{document}
    \[
        A \approx B
    \]
\end{document}

Or something else?

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marked as duplicate by Jesse, Christian Hupfer, Martin Schröder, Adam Liter, Masroor Jun 12 at 15:29

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1  
At en.wikipedia.org/wiki/List_of_mathematical_symbols it is suggested to use \sim; type \newcommand{\soom}{\sim} in the preamble and use \soom, so if you need to change the symbol you can do it in just one place. –  egreg Jun 12 at 12:52
    
I didn't know that list in Wikipedia. You may provide the answer so that I will accept it. –  cacamailg Jun 12 at 13:01
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The Wikipedia page is unreliable and does not correspond to standards. According to ISO 80000-2, the symbol created using \sim expresses proportionality, which is an entirely different thing. –  Jukka K. Korpela Jun 12 at 13:07
    
Do you have any suggestion? –  cacamailg Jun 12 at 13:11
1  
In school decades ago, we always used a script capital "O" as a mathrel that linked two items of the same order of magnitude. But I have not found a comparable looking script "O" in my brief searches of the fonts. –  Steven B. Segletes Jun 12 at 13:16
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2 Answers 2

up vote 4 down vote accepted

The list of symbols on Wikipedia suggest to use \sim (for “poorly approximates”). However one should always keep in mind that there's no world authority for mathematical symbols, so different fields could use different symbols.

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In order to be as independent as possible from a particular choice, type

\newcommand{\soom}{\sim} % same order of magnitude

and use \soom in your document. It will be easy to change the symbol by just modifying this definition.

Use the command name you prefer, instead of \soom, of course.

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I found math.uiuc.edu/~hildebr/595ama/ama-ch2.pdf, which might be what I was looking for. –  cacamailg Jun 12 at 13:46
    
@cacamailg It depends on what you mean by “order of magnitude”. Is it about physics quantities or asymptotic analysis of function? –  egreg Jun 12 at 13:49
    
It is about physics quantities. –  cacamailg Jun 12 at 14:25
    
@cacamailg So the paper you refer to has nothing to do with your problem. –  egreg Jun 12 at 14:29
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Use the “≈” character, which you can produce using \approx. It expresses approximate equality, which is not an exact mathematical concept; it depends on the context and on the point of view whether an approximation is sufficiently good.

There is no standardized or conventional mathematical symbol for “same order of magnitude”, except in the sense that this concept can be interpreted as (coarse) approximate equality.

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3  
is \approx, not \cong –  egreg Jun 12 at 13:21
    
@egreg, thanks for the correction. I’ve edited my answer. I was confused because I checked this too fast and was mislead by the Unicode name of “≅” (\cong), APPROXIMATELY EQUAL TO, which conflicts with the modern usage of the symbol (but Unicode names have been carved in stone). –  Jukka K. Korpela Jun 12 at 18:04
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