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Re: \ell

>I don't understand the purpose of the \ell glyph from a
>mathematician's point of view. My conjecture: In ancient times
>mathematicians had to use typewriters where lowercase Latin l was
>indistinguishable from the numeral 1.

In ancient times mathematicians used pencils, quill pens, slates, clay
tablets... I still find that the best tools for doing mathematics are
a pencil and paper.

I use \ell to denote the length of a sequence, for example:

... the length of the sequence $L=\langle l_1, l_2, \dots l_n \rangle$
is denoted $\ell(L)$ ...

(see: ``Abstracting a Specification from Code'', M. Ward, Journal
of Software Maintenance: Research and Practice,
Vol 5, 1993, pp 101-122, photocopies supplied on request!)

Mathematician's are always searching around for new symbols. Some of these
are constructed by starting with a letter and writing it in a different way
(epsilon used as set membership, the so-called ``blackboard bold'' N, Z,
Q, R and C used to represent sets of numbers, \Sigma used as a summation
sign, \partial, which is a variant of either \delta or d, for PDEs etc.)
Sometimes these symbols take on a new meaning of their own, and become
widely adopted.

The historical source is no guide to how these symbols should be typeset
_now_: consider the integration symbol \int which was originally a ``long s''
representing ``summation''. Since we no longer use ``long s'' we should
replace \int by the letter s right? :-)