Information Technology Reference
In-Depth Information
Mathematical symbols should, if possible, be the same font size as other characters.
For example, the expression
2 is more legible than
n
(
n
+
1
)
+
1
2
(
(
+
)
+
)/
n
n
1
1
even
though the former usesmore characters; but take carewith expressions such as
a
c
that are easy to misread. Font sizes should be consistent (though not necessarily
identical) in text and displayed equations; large symbols are ugly and tiny symbols
are illegible.
Consider breaking down expressions to make them more readable, especially if
doing so enlarges small symbols.
/
b
+
e
2
−
a
x
1
−
a
2
x
2
f
(
x
)
=
a
x
1
e
2
g
(
x
)
where
a
2
x
2
Avoid unnecessary subscripts: use
x
and
y
rather than
x
1
and
x
2
. Also, don't nest
subscripts on top of one another: the symbol
i
is legible in
x
i
, barely acceptable in
x
j
i
,
and ridiculous in
x
k
j
i
. Mix subscripts and superscripts with caution: the expression
x
p
k
j
b
f
(
x
)
=
g
(
x
)
=−
−
is a mess. Be careful with choice of letters for subscripts: in some small fonts,
the letters
i
,
j
, and
l
are not easy to distinguish.
Some mathematics should be rewritten to remove or reduce the use of subscripts.
For example, if
W
then youmight write
i
=
1
={
w
1
,...,
w
k
}
f
w
i
,
but the equivalent
expression
w
∈
W
f
w
is easier to read.
As illustrated in these examples, even simple mathematical expressions require
competent typesetting. Such typesetting may involve use of advanced word-
processing facilities, but failure to learn such facilities is no excuse for sloppy
presentation.
Notation
Ensure that the symbols you use will be correctly understood by, and familiar to,
the reader. For example, there are several symbols (including
,
and probably others) that are used in one context or another for logical implication.
These symbols also have other meanings, so there is plenty of scope for confusion.
The symbols
⇒
,
→
,
,
Ↄ
,
,
|=
∼
,
, and
≈
are all used to mean
approximately equal to
,but
∼
may
also represent an equivalence relation. The symbol
=
means
is congruent to
, not
approximately equal
. Don't be lazy; use
≤
, not
<
=
,for
less than or equal to
.
) seem to cause particular problems in
typesetting. In one of my papers the typesetters changed these to square brackets (
The symbols for
floor
(
) and
ceiling
(
[]
),
and in the process utterly destroyed the meaning of the equations. Similarly, mistakes
in placement are common with subscripts. Watch out for such errors.
Symbols such as
, and abbreviations such as “iff”, should
not be used as substitutes for words. These symbols may be compact but they are
difficult for readers to digest.
∀
,
∃
,
<
,
>
,
=
, and
⇒
