Sets and Functions

Abstract

I need hardly explain why I deal with sets after numbers. I hope I have made clear that both as regards content and as regards teaching, mathematics starts with number, with counting, and the greater part of mathematics that most people have to learn, centres around number. Set theory’s voice in the last chapters was surprisingly soft, compared with the arrogant shouting of false set theory. It is good to start with the arrogant shouting of false set theory. It is good to start with the most important things; it is reassuring to know how much less important matter is needed to do the important ones right.

Thus by the gigantic cooperation of Frege, Dedekind, Cantor the infinite was raised to the throne and enjoyed an era of great triumph… From the paradise created by Cantor, nobody may be allowed to evict us.

Set theory knows no barrier of principle between the finite and the infinite. Under this view the infinite is even simpler.

D. Hilbert, Über das Unendliche, 1927

H. Weyl, Die heutige Erkenntnislage in der Mathematik, 1925

The letter killeth but the spirit giveth life.

2 Cor. Ill, 6