Galileo's Paradox
There are exactly as many square numbers as there are numbers, even though almost every number is not a square.
163813 min read
German mathematics
Richard Dedekind
1831 – 1916
Braunschweig mathematician, the last doctoral student of Gauss, and one of the architects of modern foundations. In Was sind und was sollen die Zahlen? (1888) he turned Galileo's embarrassment into a definition: a set is infinite precisely when it can be matched one-for-one with a proper part of itself.
2 entries
Gabriel's Horn
A shape you can fill with a finite bucket of paint but whose inside you could never finish painting. How?
16417 min read