• Mathematics

    The Reality of Rational and Irrational Numbers

    In the previous post we talked about the problem of mathematical realism of negative and complex numbers; the issue was that you can construct these numbers logically and conceptually, but you will never find them in the real world. The problem of irrational numbers is the opposite: you can easily find irrational numbers such as √2, π, and e in the real world, but they appear to have infinite irreducible complexity. Similarly, many rational numbers such as 1/3 have infinite digits in them. Unlike negative numbers which are fully understood but never seen, rational and irrational numbers are seen but never fully understood. In what sense are these numbers then…