Numbers, Vectors and Matrices

Abstract

It is a fair bet that your first conscious introduction to mathematics was when you learned to count: one apple, two apples, and so on. Well, professional mathematicians too start their activities by setting up a counting system. There is one slight difference between the system they adopt and the system you became familiar with: they include the number zero at the beginning. (Zero apples is a perfectly sensible counting number; it is, in fact, exactly the number of apples I have eaten so far today.) This system, the sequence

$$ 0,1,2, \ldots , $$

((1.1))

is called the natural numbers. The natural numbers form such a useful system that they are given a special name: ℕ.