190Tutorial6

Tutorial 6

• With Stephen and Nick

Mindscape 21, §3.1 of text

Suppose you have a finite number of pigeons and a finite number of holes. You try a method of assigning pigeons to holes and, after filling all the holes, some pigeons remain. If you remove the pigeons and try again, is there any hope of placing each pigeon in an individual hole the second time? Suppose you have an infinite number of pigeons and holes. Is it possible that a first attempt to give each pigeon an individual hole fails but a second attempt succeeds?

If, after filling a finite number of holes with pigeons, and there is a finite number of pigeons still to be placed in the holes, the method used to assign the pigeons to the holes is irrelevant. No matter what method is used, each pigeon will never have a unique hole.

It is not possible that a first attempt to give each pigeon an individual hole fails and then a seccond attempt succeeds.