Re: Cantor Diagonal Proof

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
[...]

I don't have to google anything: if you can multiply an infinitesimal by
0.5 then it isn't an infinitesimal -- it was twice as large as another
real and all real numbers can be multiplied by 0.5.

Infinitesimals are not real numbers.

There are number systems that include infinitesimals in addition to all
the real numbers, and that are internally consistent.  The rules can
vary from one such number system to another, so there's probably no one
answer to what happens when you multiply an infinitesimal by 0.5 in such
a system.

If you're interested in learning more, search for "surreal numbers" or
"hyperreal numbers".  If you're not, don't.

--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
void Void(void) { Void(); } /* The recursive call of the void */