On one hand, there are countably many definitions. Each definition can be written on computer in a text file; now take its binary form as a base-256 integer.
On the other hand, Cantor’s diagonal argument applies here, too. I mean, for any countable list of definable real numbers, it provides a definition of a real number that is not included in the list.
How many real numbers can be defined?
On one hand, there are countably many definitions. Each definition can be written on computer in a text file; now take its binary form as a base-256 integer.
On the other hand, Cantor’s diagonal argument applies here, too. I mean, for any countable list of definable real numbers, it provides a definition of a real number that is not included in the list.
Funny, isn’t it?
(solution)