Sunday 25 December 2016

soft question - Acronyms and words as variables and in mathematical notation

I am unsure if this question is warranted.




Often mathematical symbols and objects are represented by a single character, e.g. variables are most often single characters like $x$, and often to describe a variable further we use an additional character in a subscript or a superscript, like $x_t$.



In physics people often choose intuitive letters to represent quantities as variables, for example, using $t$ for time or $v$ for velocity (starting character is used to make it more recognizable).



Of course this always isn't the case and I acknowledge that there are the cases of function names such as $\sin(x)$ or even objects like $\sup A$ and $\inf A$ for a set $A$.



However my question is what is the general opinion (concerning formal formatting) on using words, abbreviations, and acronyms as variable quantities in mathematical sentences.







An example, we have that the revenue of a simple trade of a good is the quantity multiplied by the price. A few possible formats include:




  1. $R = q\times p$

  2. $\text{revenue} = \text{quantity} \times \text{price}$

  3. $r = q_{\text{good}} \times p_{\text{good}}$



Perhaps #3 isn't so pretty with this simple formula, but if we take the mark-to-market formula of quantity times the difference in market price and trade price, we can get some other formats:





  1. $\text{MTM} = q\times(p_{\text{market}} - p_{\text{trade}})$

  2. $\text{MTM} = q\times (\text{MP} - \text{TP})$



and so forth.



Of course I see words and acronyms often in the equations from the softer sciences like economics where my example comes from, but I am sure this question applies to pure mathematics in some cases.







I do not know which notation style we should tend towards these cases, especially if it was in the context of an academic paper.



Thanks for any opinions!

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