off topic but please forgive me me and answer

[MRAB]

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").