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I guess this is a very basic question, but I want to get this right:

I have a result, e.g.,

$$c=\frac{1+r-546u\sqrt{h-8+7}}{b+3+f}.$$

Now I want to discuss the numerator and denominator separately in a paper in a 'correct' way. First, we inspect the numerator and check whether it is positive:

$$ f(r,u,h)=1+r-546u\sqrt{h-8+7}\ge0.$$

However, I am introducing this now as a function, which seems a little odd to me. Isn't there something more generic instead of $f(r,u,h)$?

Similarly, I might have a function with multiple terms and want to inspect the properties of these terms separately:

$$k=(1+r)^2-546u\sqrt{h-8+7}.$$

What is the best practice to refer to these terms?

Xander Henderson
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Karl A
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  • I mean, it’s pretty arbitrary. You could call it $(*)$ for instance. – Vishu Mar 06 '20 at 16:39
  • If you are doing something sufficiently complex with the numerator and denominator, then sure, you should give them names. If all you are doing is reasoning about them, in such a way that you don't need to repeat the expressions for $f$, $g$ in long formulas, I would just label them (1), (2). – Jair Taylor Mar 06 '20 at 18:09
  • Thanks and sorry for the late reply! Can you please given an example, provided I do something sufficiently complex? As in "first, we inspect the numerator, f(x)=(...)" @JairTaylor. – Karl A Mar 09 '20 at 09:14
  • How would this look like in your case @TavishMusic? Like this: "first, we inspect the numerator, (*)=(...)" – Karl A Mar 09 '20 at 09:15
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    @KarlA Pretty much. I would call the numerator $()$ and the denominator something like $(\blacktriangle)$ and then reference them like $\frac{()}{\blacktriangle} = f(x)$. – Vishu Mar 09 '20 at 09:26
  • @TavishMusic That's a non-standard usage that will look a bit strange. For one, other symbols like $\blacktriangle$ are not usually used. You can use * or ** for up to two or so equations, otherwise you should number them (1) (2) etc. or possibly (2.1), (2.2) etc for equations in Section 2. Furthermore, these symbols should not take the place of variables or functions in an expression. They are only used in English sentences: e.g., "Then from (1) we obtain..." or "Then the denominator of (3) is..." – Jair Taylor Mar 09 '20 at 15:20
  • If you have to do anything more complex than what can be written easily in an English sentence, you need to assign appropriate functions or variables to these expressions. You can say something like "Then dividing (1) by (2) we obtain..." but not "Then (1) / (2) = ..." except maybe on a blackboard. – Jair Taylor Mar 09 '20 at 15:25

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