# Mathematics Style Guide - l vs 1 vs |

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?

• Try to imitate $\ell \mid 1$ as closely as possible by hand :) – Rahul Mar 26 '11 at 19:50
• It is interesting how doing mathematics has changed my handwriting. I always used to confuse my "2" and my "z", so I started writing my 2's with a curl at lower-left and my z's with a strike-through. I usually writes my l's (as in "late") as Rahul above. – Fredrik Meyer Mar 26 '11 at 20:11
• caligraphy.stackexchange.com ? – Raskolnikov Mar 26 '11 at 21:25

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 $\mathcal{e}$.

• I agree completely. I've had to modify my handwriting as well. I started using curlier letters to distinguish, for example, $4$ from $y$ and $\times$ from $x$. After a little while, of course, I got used to it. – Abel Mar 27 '11 at 5:59
• I learned a lot of my algerba in a German Junior High, in my experiance Germans almost always cross their 7's and z's, in addition they draw 1 with an exadurated serif like digonal at the top (like a lazy 7) since the 7's are crossed this gives a nice uniquenes to pretty much everything. – tletnes Jan 3 '13 at 22:42
• When I was in high school, a math teacher asked one hapless student to go to the board to write “eks times eks times eks”. What appeared on the board looked like $\times\>\times\>\times\>\times\>\times$. – Lubin Sep 16 '13 at 18:12

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.

• Thanks. I guess I'll just have to slow down when I'm writing stuff :-) – maximilienwolfgang Mar 26 '11 at 19:58

Another approach is to write the 1 serifs backwards (mirror image). That way, the top serif can be exaggerated, but doesn't look anything like a 2 or 7. Just make it pointy so it doesn't look like a C.