# My good practice concerning inline mathematical formulas

I am not sure whether this is common practice, but I do feel there is a benefit from what I'm going to discuss next. If you feel otherwise about this particular good practice I tend to use in my documents, do not hesitate and tell me why :-).

## Problem sketch

When typing a mathematical text you use inline mathematical formulas. When doing this without much thought, *i.e.*, not caring about non-breakable spaces (or ties), also known as `~`

you end up with nasty results.. Exercise 18.10 of the TeXbook tries to make you aware of these so-called *bad line breaks*.

But Knuth doesn't really describe the rules he tends to follow and my personal taste differs from what he suggests as a solution to the given exercise. My main concerns are:

- lines starting with a symbol
- line breaks inside inline mathematical formulas
- symbols denoting an object at the end of a line while the type of object is on the next (as in: Let
*C*be a commutative ring)

Number 3 is something he avoids, but 1 and 2 are phenomenons that will occur when following his technique (as is shown in the typeset solution). And he advocates the usage of white spacing to denote formulas, a practice that has gotten out of use since then. Now what I want to discuss in this post are the ways how I avoid these three problems.

## Solutions

The first one is obvious: you just prefix each inline math formula with a non-breakable space `~`

. No more line breaks will happen at this point now. This same technique applies to the third one: just suffix each introduction of a symbol with a non-breakable space.

This introduces a problem that concerns the second one as well: line breaking. When TeX is offered *less* opportunities to break a line, the results tend to get poorer. And I want to make it even worse: I don't want *any* line breaks within formulas! They're ugly!

How do I avoid line breaks in inline mathematical formulas? By putting `\relpenalty=10000`

and `\binoppenalty=10000`

. This prevents TeX from breaking inside formulas because it would involve infinite badness (yes, infinite is at 10000): breaks at both relationships (equal signs and the like) or binary operators are forbidden. This is kind of like the `-Werror`

flag in `gcc`

: all warnings (split formulas) are treated as errors (bad boxes). TeX is only allowed to break in text and if that would introduce intolerable badness I get to solve it myself. What's nice about this solution is that it is unobtrusive: one could also put `\mbox{}`

around each formula but that would be *bad*.

There are two solutions to the problem of the bad boxes introduced by this practice:

- rewriting your text, opting for a less symbolic and more prosaic writing
- putting formulas in display style

I feel both solutions tend to improve a mathematical text when applied the correct way. When typing you get the opportunity to be more verbose: handwritten math often contains many implicit facts due to the fact that it takes more time to write, a TeX'ed manuscript can offer a bit of explicitation by adding little words and slightly redundant phrases. And in order to avoid having a densely written roman-style of mathematical manuscript, display style can break the flow in a good way.

## Morale

- use ties, the TeXbook explains how, but bear in mind your own personal taste
- prevent line breaks inside formulas by adding

## My answer to the exercise

I prefer the prose of the second suggestion more, so I've TeX'd it how I would do it.