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128 Risk management technology in financial services
at large are all about. Systems and rules, however, only make sense in a domain
of mathematical concepts taken as an integrated system, to which the next section
addresses itself.
7.4 Notion of a mathematical system
In 300 BC the Greek philosopher and mathematician Euclid gathered together
the geometrical knowledge then available, consisting of the Pythagorean and other
theorems, and combined that knowledge into a system. The concepts and linkages
characterizing Euclid’s approach have become the model for all scientific systems.
The main characteristic of Euclid’s system is the setting off of some theorems as
postulates or axioms,
The hypothesis Euclid made is that from these basic theorems and all postulates,
remaining theorems may be derived by logic.
It is important to appreciate that postulates or axioms do not necessarily imply a
self-evident truth. Basically they are man-made assumptions, and therefore tentative
statements. As long as these statements are not self-contradictory, this is acceptable
because as a system of signs and rules mathematics is man-made. This being said, the
process of system making is itself very important and requires further discussion.
In mathematics the word system usually means a series of laws.
In the physical sciences, however, it means a portion of the universe around which
we can draw imaginary boundaries for the purpose of study of what is enclosed
within them.
In the present discussion the word system will be assumed to mean an organized
working total; a group of interdependent elements united by a common objective. By
this token, system analysis is an attempt to determine the best way to achieve that
objective while the definition of analysis at large is much broader, as we saw in
section 7.3.
Systems may themselves be subsystems of other larger systems. In most engineering
studies as well as in finance, the idea used in the physical sciences of drawing an
imaginary boundary holds. For any practical purpose of analysis,
A system is not just a sum of elements superimposed like sand grains in a hill of sand.
To be a system, the aggregate must have an organizational structure, and the
interaction among its elements must be well defined.
Furthermore, the way to bet is that a system is made to serve some purpose.
Systems receive an input, have a characteristic throughput and give an output. This
sentence is of fundamental importance, even if it does not imply any value or degree
of desirability as to the output of a system, neither is it guaranteeing that there will
be an output.

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