[texhax] le vs leq and \ZZ vs \Z

[Barbara Beeton]

dear konstantin,

    1. I'm using LaTeX for quite some time now and have always wondered why
    there are two possibilities to typeset the "less or equal than" symbol.

    Why are there two commands "le" and "leq" to typeset the same symbol?
    Is it just for historical reasons or is there a "proper" way to do it?

the choice of which to use is usually
what is known as "house style"; in
most situations, the single or double
horizontal rule doesn't change the
meaning, but some publishers prefer
the single, and some the double rule.
(some mathematicians also have strong
preferences.)  so you could say it's
historical.

there's also a form in which the "equal
rule" is parallel to the lower arm of
the less-than.  again, mostly "house
style" or author preference.  but if
the rule is parallel to the upper arm
(equal or less than"), i've seen one,
two, and even three parallel rules
denoting different orders of a relation
that (not being a mathematician) i don't
really understand.  but i've spent
several years presenting published
examples of such symbols to the unicode
technical committee as documentation
supporting their addition to unicode,
so these statements are on firm ground.

    2. Along the lines of "doing things properly":  There are certainly lots
    of people out there who use on of the two following macros

    \DeclareMathOperator{\ZZ}{\mathbb{Z}}
    \DeclareMathOperator{\Z}{\mathbb{Z}}

    to typeset integers.  While the second one is shorter, a friend of mine
    warned by about one-letter-macros labelling them "bad style".
    Do you agree?

i agree that using one-letter-macros is
"bad style".  but there's a solid reason:
plain.tex (knuth's "starter set") contains
definitions for many single-letter commands,
and these are taken over intact into latex.
because many of them are commands for
accents, which are treated differently with
different encodings and fonts, some packages
(notably hyperref) redefine them with the
assumption that they will still retain the
original meaning.  since even reasonably
experienced texers don't always remember
all of the one-letter commands, it's easier
and better to avoid problems by not defining
your own versions.

there are also quite a few "predefined"
2-letter commands, but most of them are
better known (by a u.s. audience) than
the 1-letter commands, and not as often
redefined by packages.
							-- bb