Page 19 - Becoming Metric Wise

8 Becoming Metric-Wise

Yet, as observed in Zhang et al. (2013), in other fields metrics are often
understood as statistical techniques, while in the information sciences sta-
tistical techniques are just a part of a more general notion. As stated
above, this more general notion is in our view best described as
informetrics.
Informetrics, and especially visualization techniques as used in infor-
metrics, together with the sociology of science are important subdomains
of the science of science, the scientific study of science itself.

1.5 MATHEMATICAL TERMINOLOGY

We end this chapter by providing some basic mathematical terminology
and notation used throughout the book.

1.5.1 Numbers
We distinguish the following number sets (the term set is defined in
Subsection 1.5.3).
The natural numbers, denoted as N or N. This is the infinite set
{0,1,2, .. .}. If the number zero is excluded we write N 0 or N 0 5 {1,2,3,
.. .}. These are the strictly positive natural numbers.
The set of integers, denoted as Z or Z, consists of the natural numbers
and their opposites, i.e., {0,1, 21,2, 22, .. .}.
The set of rational numbers, denoted as Q or Q, consist of all num-
bers that can be expressed as the quotient or fraction a/b of two integers,
a and b, with the denominator b not equal to zero. The number a is called
the numerator. If b 5 1 the rational number is an integer.
We recall the following important relations:
a c
If b and d 6¼ 0 then 5 3ad 5 bc
b d a c
If b and d are strictly positive then , 3ad , bc.
b d
Finallywehave the set ofrealnumbers R or R.Realnumbers can
be thought of as values that represent a quantity along a continuous line.
Real numbers which are not rational numbers are called irrational num-
p ffiffiffi
bers. The numbers π 3.14159 and 2 1.4142 are examples of irra-
tional numbers. Irrational numbers never result directly from counting
operations, but the real numbers, including the irrational numbers, are
used when modeling informetric data. An important reason for using
real numbers is that they contain all limits of sequences of rational num-
bers. Somewhat more precisely, every sequence of real numbers having