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Can someone tell me whether I can express $$a ≈ 922\text{ trillion}, a > 922\text{ trillion}, a = 922,337,203,685,477.5808$$ using the following notation:

Possible way to abbreviate notation for relations operating on the same LHS

in a mathematical text?


If I can't, can someone tell me an abbreviating notation similar to this notation, that can be used?

Background

I'm asking these questions in relation to simplifying mathematical expressions on the new Data type summary page for the VBA programming language. In particular, various ranges are specified for different data types, and I want to improve general readability of these ranges, especially in regard to comparing the ranges.

The reader may want to simply read a ball-park upper-limit figure for a range, which is why '922 trillion' is in the text. It is easier to read than the precise upper limit, & this may be all that a reader is interested in. At the same time, some readers may want to know the exact upper limit.

I'm not so concerned about readers not being able to straightaway read any notation that I use, as I'm considering hyperlinking to verbose English-language interpretations for each of the mathematical texts on the page.

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  • $\begingroup$ I've seen $a\lesssim b$ or $a\lessapprox b$. for the first two. Never seen a notation that covers all three. $\endgroup$ – lulu Jun 12 at 12:10
  • $\begingroup$ The syntax is "\lesssim" or "\lessapprox" $\endgroup$ – lulu Jun 12 at 12:10
  • $\begingroup$ @lulu, that's great! I tried to look for examples of such on the web but couldn't find any. I'm a software developer (not a mathematician). Do you have any hyperlinks demonstrating the use of ≲ & ⪅ in mathematical texts? $\endgroup$ – Mark Fernandes Jun 12 at 12:13
  • $\begingroup$ Well, I've found this question here, which mentions it...though, as you'll see from the posts and comments there, it's hardly standard. I think that people would understand it if it was used, which is the key point (though were I to use it, I'd probably define it at the time). $\endgroup$ – lulu Jun 12 at 12:16
  • $\begingroup$ Thanks for the tip @lulu. $\endgroup$ – Mark Fernandes Jun 12 at 12:44
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I don't think you should use invented notation. Although your reader would understand you , it is strange.

It is not at all clear why you are trying to say this. Apparently you have a precise value for a large number and also an approximate inequality, Which of these is important? Do you mean

I know this $15$ digit number to four decimal places of precision but all that matters is that it's almost $923$ trillion.

or

This number that's almost $923$ trillion has now been measured to four decimal places of precision.

My advice: be kind to your reader. Use more words instead of looking for compact notation that has to be deciphered.

Edit in response to comment

For the kind of documentation you are writing I think a display as in your image is fine (iat would not be in a math paper). As @lulu suggests, use $\lesssim$ or $\lessapprox$.

A comment in the Range field like

An approximate bound for $a$ and its exact value:

might be useful.

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  • $\begingroup$ Re. "It is not at all clear why you are trying to say this. ..", please see my updated question which now explains why. Re. 'which of these is important' from your post, I would say neither. I think we are having different insights because I'm asking these things in regard to computer programming documentation, whereas you are probably looking at this more from a perspective of how mathematical papers should be expressed. Thanks for the tip re. kindness to my reader. $\endgroup$ – Mark Fernandes Jun 12 at 12:42
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That’s weird but I get what you’re saying. How about $$a = 922\,337\,203\,685\,477.5808 > 922\text{ trillion} \approx 922\text{ trillion}$$ and/or $$\begin{align} a &= 922\,337\,203\,685\,477.5808 \\ &\gt 922\text{ trillion} \\ &\approx 922\text{ trillion} \end{align}$$

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  • $\begingroup$ thanks for this. Your second example interests me the most. Is it possible to start the example with 'a ≈' or 'a >' instead of with 'a ='? $\endgroup$ – Mark Fernandes Jun 12 at 14:31
  • $\begingroup$ @MarkFernandes Yeah definitely. You can even put $a$ on each line. $\endgroup$ – gen-z ready to perish Jun 12 at 14:34
  • $\begingroup$ @MarkFernandes Don’t forget to upvote or give the $\color{green}\checkmark$ to answers you like $\endgroup$ – gen-z ready to perish Jun 12 at 14:34
  • $\begingroup$ Great, this is definitely useful. Thanks. Unfortunately, I don't have enough status at the moment to up-vote your post. Otherwise, I would up-vote your post. $\endgroup$ – Mark Fernandes Jun 12 at 14:35
  • $\begingroup$ Another question for you. I noticed that you used spaces instead of commas when writing the precise figure for 'a'. Can you tell me whether this is readily understood by mathematicians? I looked on the internet to see whether such display formats could be used but couldn't find any supporting texts for it. Would probably make the numbers more readable if I could do this. $\endgroup$ – Mark Fernandes Jun 12 at 14:46

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