off topic but please forgive me me and answer

[Patrick Maupin]

On Apr 3, 12:39 pm, MRAB <pyt... at mrabarnett.plus.com> wrote:
> Patrick Maupin wrote:
> > On Apr 3, 11:59 am, Emile van Sebille <em... at fenx.com> wrote:
> >> On 4/3/2010 8:46 AM Patrick Maupin said...
>
> >>> On Apr 3, 9:43 am, "Martin P. Hellwig">  IMHO, the crackpot in this
> >>> regard is actually partially right,
> >>>> multiplication does mean that the number must get bigger, however for
> >>>> fractions you multiply four numbers, two numerators and two
> >>>> denominators. The resulting numerator and denominator by this
> >>>> multiplication get indeed bigger.
> >>> That argument is great!  Just make sure that you've managed to leave
> >>> before the class has to learn about irrational numbers that don't
> >>> *have* numerators and denominators ;-)
> >> Ahh, but no ones arguing that irrational numbers don't get bigger --
> >> even before you multiply them!
>
> > True, but being an optimist, just as (-1 * -1 == +1) (which
> > admittedly, I had a hard time trying to explain to my father years
> > ago), and just as (not not True == True) and just as multiplying two
> > imaginary numbers can have a real result, I was hoping that it would
> > also be the case that having a discussion with an irrational person
> > about irrational numbers could have a rational result.  Of course,
> > that hope was incredibly naive of me, since most operations with
> > irrational numbers which do not involve either closely related
> > irrational numbers or zero will also result in irrational numbers.  I
> > think induction will show that this property (that an irrational
> > number can make any result that it is involved in irrational) can also
> > be applied to irrational people and discussions.  ;-)
>
> The square root of 2 is irrational, but if you multiply it by itself
> then the result isn't irrational, so not all operations involving
> irrational numbers will result in an irrational result (unless that's
> what you mean by "closely related irrational numbers").

Yes, I think I am closely related to myself.  But in addition to that
particular disclaimer, I qualified the statement with "most" and I
also mentioned that zero is special.  I stand by the assertion that if
you take a random assortment of non-zero numbers, some irrational,
some rational, and a random assortment of numeric operators, that most
operations involving an irrational number will have an irrational
result.

Regards,
Pat