THE RELATIONS OF MAGNITUDE OF CARDINAL NUMBERS
The theorems of cardinal arithmetic are frequently used in ordinary
conversation. What is known as the Schroeder-Bernstein theorem was used,
long before Bernstein or Schroeder, by Edward Thurlow, afterward the
law-lord Lord Thurlow, when an undergraduate of Caius College,
Cambridge. Thurlow was rebuked for idleness by the Master, who said to
him: "Whenever I look out of the window, Mr. Thurlow, I see you crossing
the Court." The provost thus asserted a one-one correspondence between
the class A of his acts of looking out of the window and a part of the
class B of Thurlow's acts of crossing the Court. Thurlow asserted in
reply a one-one correspondence between B and a part of A: "Whenever
I cross the Court I see you looking out of the window." The
Schroeder-Bernstein theorem, then, allows us to conclude that there is a
one-one correspondence between the classes A and B. That A and B were
finite classes is not the fault of the Master or Thurlow; nor is it
relevant logically.