Information Technology Reference
In-Depth Information
(
,
)
=
{
|∃
,
:
=
∧
=
}
Here, gcd
x
y
max
z
u
v
x
uz
y
vz
Here, the value gcd
(
x
,
y
)
is the largest integer that is a divisor (or factor)
of both
x
and
y
.
As this example also illustrates, clear writing rather than mathematics may be prefer-
able for explanation of a familiar concept.
But don't replace symbols by words unnecessarily; for example, write “
a
b
”
rather than “
a
is less than or equal to
b
”. Concocted or amusing symbols are not
a good idea; don't use
≤
as an operator, for example. Use each operator for one
purpose only; compilers may understand overloading, but people do not.
Don't re-use notation: an excellent way of confusing readers is to use
N
for one
quantity on page 6 and for another on page 13. But expressions with similar meaning
should have similar notation that follows consistent rules. Adhere to conventions
such as using
i
and
j
for integer subscripts and calligraphic letters for classes. And
don't vary an existing notation without good reason.
Take care with accents. Don't use
♣
a
,
dž
a
,
ǜ
a
, and
¯
a
together. Statistics texts sometimes
use formulations such as
¯
dž
a
—the mean of the estimator of
a
—but this is better avoided
by reformulating. And don't pile up primes: the symbol
a
may be clear, but what
about
D
l
i
? Some authors put powers on primes, as in
a
4
to represent
a
, but this
notation is often unclear. If you have such deep primes, consider reworking your
notation to get rid of them.
Ranges and Sequences
The closed range of real numbers
r
where
a
≤
r
≤
b
is represented by “
[
a
,
b
]
”; the
open range
a
<
r
<
b
is represented by “
(
a
,
b
)
”; the range
a
≤
r
<
b
is represented
by “
”.
It is common practice to use an ellipsis to describe a sequence of integers; thus
[
a
,
b
)
”; and the range
a
<
r
≤
b
is represented by “
(
a
,
b
]
m
n
represents all integers between
m
and
n
inclusive. An infinite sequence is
usually represented by
m
1
,
,...,
, where it is assumed that the reader can extrapolate
from the initial values to the other members of the sequence. Thus “2
m
2
,...
” would
be assumed to be the sequence of positive powers of 2. Always state both the lower
and the upper bound if the sequence is finite and ensure that the intended sequence
is clear.
An expression such as 1
,
4
,
8
,...
≤
i
≤
6 should be replaced by
i
=
1
,...,
6ifitisnot
clear that
i
should be an integer.
Some computer scientists, particularly in the context of computing theory, rep-
resent 1
1, to mimic
the behaviour of programming languages such as C. Your usage should be made
clear; unexplained notation, even if common in the specific field of the paper, is
unnecessarily exclusive.
,
2
,...,
n
by
[
n
]
. Others let
[
0
,
n
]
stand for 0
,
1
,
2
,...,
n
−
