Two letter variable names

Question

In math mode, TeX assumes "hidden multiplication" (so that two variable names put nearby have invisible multiplication between), so that, AFAICT, expressions like $ABC$ are rendered with small distances between letters.
Now, what to do if I have a two-letter variable name, like for instance TP or FN (true positive or false negative)? Leave as they are? Put them in \text? Yet in the first option they will look like T*P or F*N and in the second one they will differentiate from one-letter symbols.

In optics, the 2-letter variable NA is used for numerical aperture.

Answer 1

You would write \mathit{TP} or \mathit{FN}. If you're going to do this frequently, you can make macros for them.

\newcommand\TP{\mathit{TP}}
\newcommand\FN{\mathit{FN}}

Answer 2

I guess that the best solution is to define a macro with manually adjusted negative space, e.g.

\newcommand\TP{T\!P}

or with \hspace{-0.1em} instead of \!. You can also use the \ric command from this answer of mine to remove the space after the T. (Then you won't have to guess the amount of negative space, but the result is not always satisfactory.)

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As there's been some debate about this answer, let me provide more detail:

It is not the case that TeX puts space between the letters in math mode, but after each letter it puts the italic correction for the letter. There are ways to see what's happening, and both are a bit steep.

First possibility: On a console, run

tex '\tracingall $TP$ \bye'

If you are on a unix like system, better run

tex '\tracingall $TP$ \bye' | sed -n '/mathon/,/mathoff/p'

Then in the terminal output you'll find the lines

...\mathon
...\teni T
...\kern1.3889
...\teni P
...\kern1.3889
...\mathoff

The \tracingall command is telling TeX to, well, leave a trace of everything it's doing. The first 3 of these lines tell you the following: Math mode is entered, the letter T in font \teni (10pt math font cmmi10) is typeset, and then a kern of 1.3889(pt) is put after the T. This is exactly the italic correction of the T. How do I know this? On a unix system that's easy: Run

tftopl $(kpsewhich cmmi10.tfm) | grep 'CHARACTER C T' -A3

(tfm means "TeX font metric") and you'll get the terminal output

(CHARACTER C T
   (CHARWD R 0.584376)
   (CHARHT R 0.683332)
   (CHARIC R 0.13889)

This tells you the following about the character T in the font cmmi10: It has a width of 0.584376, a height of 0.683332 and an italic correction of 0.13889, all measured in pt.

The same applies to the lines above starting with ...\teni P; the letter P has the same italic correction, and then mathmode is turned off. Though this looks convincing, it doesn't prove that the \kern1.3889 provided by \tracingall comes from the italic correction. If you want to be fully convinced, then there is no other choice than to read Appendix G of the TeXbook really extremely carefully, which I regard the steeper path.

Second possibility:

Read Appendix G of the TeXbook. Unfortunately, this is not exactly what I'd call easy reading. You get a first approximation of the insertion of the italic correction on page 441:

We frequently need to execute a subroutine called “Set box x to the so-and-so field in style such-and-such.” This means (a) ... (b) if the field contains a symbol, x is set to an hbox containing that symbol in the appropriate size, and the italic correction for the character is included in the width of the box; ...

In the current circumstances, e.g. the letter T is such a symbol that is put into the box x, together with its italic correction. However, this is not the full truth. There is one circumstance where TeX doesn't insert the italic correction: In Rule 17 on page 445 it says

If the symbol was not marked by Rule 14 above as a text symbol, or if \fontdimen parameter number 2 of its font is zero, set δ to the italic correction; otherwise set δ to zero.

We don't have to care about Rule 14 and text symbols. Why? One important feature of a math font is that its \fontdimen parameter number 2 is zero. For cmmi10, you can convince yourself by typing

tftopl $(kpsewhich cmmi10.tfm) | grep FONTDIMEN -A2

which yields the output

(FONTDIMEN
   (SLANT R 0.25)
   (SPACE R 0.0)

and you see that the second parameter SPACE is indeed zero. This makes sense: As every novice in TeX and friends has to learn, spaces don't get typeset in math mode.