Mathematics Style Guide - l vs 1 vs |

Question

I had a quick look around here and google before, and didn't find any answer to this particular question, and it's beginning to really irritate me now, so I'm asking here:

How is one supposed to write l (little L), 1 (one) and | (pipe) so that they don't all look the same? One of my teachers draws them all as vertical lines and I have seen things like |l| written as 3 vertical lines.

I tried writing a cursive l, but they always look like e when I write them, which is a whole new problem.

So is there a "best way" to write all of these on paper, or a "least confusing" way?

Thanks in advance guys ^_^

Answer 1

Personally, I always use a script lower-case L and never a print lower-case L in mathematical expressions (my handwriting is such that my lower-case E is sufficiently short and non-script-like that confusing the two is not an issue). As to one versus vertical bar, I typically make my vertical bars extend slightly above and below the line of text, but I also will draw the serifs on the one (the crossbar at the bottom and the hook at the top) if there's the potential for confusion.

Answer 2

Sometimes one has to modify one's handwriting. When I started taking math courses in college, I realized that writing "$\mathsf{x}$" and "$\mathsf{y}$" both as two strokes just led to frequent confusions. I purposely started writing $\mathcal{x}$ instead of $\mathsf{x}$, and $\mathcal{y}$ instead of $\mathsf{y}$; I also started putting "bow-ties" in my sevens (to differentiate them from $1$), and my zeds. It took a lot of conscious effort at first, now it's second nature.

I don't usually worry about $1$ and $|$, since the latter symbol does not often occur. When there is danger (e.g., number theory), I tend to write the pipe much larger, extending well below the "baseline" (e.g., $ab\Bigm| 173$), and to put the serifs on the $1$. In formulas, I always use $\ell$, even when writing things like "log" and "lim". So I write $\ell\mathrm{og}$, $\ell\mathrm{n}$, and $\ell\mathrm{im}$ (only more "vertical", with no italic slant), and use $\ell$ when it's a variable. The cursive should be tall so it's not confused with $\mathcal{e}$.