Mathematics: Rational or Irrational?

Perhaps the most basic idea in all of mathematics is that of counting numbers—the positive whole numbers. If human beings are to get interested in anything mathematical, then we should not be surprised to find them beginning with these counting numbers—their patterns of odd and even; the squares, cubes, and higher powers; the triangular numbers 1, 3, 6, 10, 15,...; the primes; the divisors of a given number and its factorisation as a product of primes; and many other fascinating properties (see, for example, Exercise 2).