On Tue, Jul 21, 2015 at 7:10 PM, Marko Rauhamaa <ma...@pacujo.net> wrote:
> This is getting deep. It is an embarrassing metamathematical fact that
> numbers cannot be defined. At least, mathematicians gave up trying a
> century ago.
>
> In mathematics, the essence of counting a set and finding a result n,
> is that it establishes a one to one correspondence (or bijection) of
> the set with the set of numbers {1, 2, ..., n}.
> <URL: https://en.wikipedia.org/wiki/Counting#Counting_in_mathematics>
AIUI, zero is defined as the cardinality of the empty set, one is
defined as the cardinality of the set containing the empty set, two is
defined as the cardinality of the set containing the empty set and the
set containing the set containing the empty set... which makes
mathematics the only language *more verbose* than the Shakespeare
Programming Language in its definition of fundamental constants.
ChrisA
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