07-11-03 21:26, gvogar wrote:
> Rusian 40 is quite diferent that other numerals.
> Are the numbers 4, 7 and 17 somehow special?
>
> How the 17 get special status? It wasn't after Gaus 17-gon
> construction.
Why "17"? Did anyone menton "17"?
Anyway, every natural number is special, including 87492335017. The
proof is by reductio ad absurdum:
Let's assume that there is at least one nonspecial natural number. Let's
consider the set of all such numbers. Since any nonempty set of natural
numbers must have a minimal element, let N be the smallest nonspecial
number. Being the smallest nonspecial number makes N special. Since N
can't be both special and nonspecial, N doesn't exist. This means that
the set of all nonspecial natural number is empty. Therefore, every
natural number is special. QED ;-)
Piotr