Introduction to Mathematical Thinking

by Keith Devlin

The Banach–Tarski Paradox, for example, says you can, in principle, take a sphere and cut it up in such a way that you can reassemble it to form two identical spheres each the same size as the original one.

A function, according to Dirichlet, is any rule that produces new numbers from old. The rule does not have to be specified by an algebraic formula.

This definition legitimizes functions such as the one defined on real numbers by the rule: If x is rational, set f(x) = 0; if x is irrational, set f(x) = 1.

ϕ ∨ ψ

typo

not−ψ

Typo?