Literal Numbers
The “Point” of Algebra
There are a number of important advantages to developing skill
in working with literal symbols to represent numbers. Among them
are
(i) We can write numerical relationships very concisely. Thus,
the formula
for the area of a circle is shorthand for the recipe: “to
calculate the area of a circle, raise its radius value to the
second power and then multiply the result by the constant
3.141592653589793 or so.” The algebraic formula makes it
much easier to see the precise nature of the relationship between
A and r here.
(ii) We are able to simulate arithmetic operations involving
numbers whose values we don’t know at present. This makes it
possible to analyze and solve all sorts of problems involving
numerical values that would be impossible to solve by any other
means. The rules for carrying out this arithmetic with symbols
are based directly on the rules for doing arithmetic with
ordinary numbers, because, after all, the symbols just represent
ordinary numbers. Most of “algebra” is just learning or
practicing strategies for doing this sort of symbolic arithmetic.
The development of science and technology, and most ongoing
research and development work today would not be possible without
an ability to represent numerical values symbolically. Skill in
working with such symbolic representations is absolutely
indispensable for working in nearly every technological field
today.
