🚀 go-pugleaf

In article <5gmqsn$bs8@milo.vcn.bc.ca>, Mark Gibson <mgibson@vcn.bc.ca> wrote:

>Incidentelly I'm sure it must have ocurred to someone that there are
>DEGREES of irrationality among the irrational numbers. For axample some
>irrational numbers when subjected to a simple operation can be mapped to a
>rational number. e.g. sqrt(2)*sqrt(2) = 2. Whilst as far as I know e*e and
>pi*pi, e*pi, etc are still irrational. Since this ocurred to a
>mathematical dunce like me it can't be that important but I though it was
>interesting, so there.

It sure has--e, pi, etc. are "transcendental" numbers, a subset of
irrational numbers.  sqrt(2), sqrt(3), etc. are "algebraic" numbers.
An algebraic number can be a root of a polynomial equation.  A
transcendental number can't.  And actually it wasn't too long ago
(relatively speaking) that pi and e were proven to be transcendental
numbers.  So it's very interesting, actually.

--Mark

-- 
Mark Meiss (mmeiss@indiana.edu)  |  No eternal reward will
Indiana University CS Dept.      |  forgive us now for     - Jim Morrison
Bloomington, Indiana, USA        |  wasting the dawn.