On Apr 3, 12:39 pm, MRAB <pyt...@mrabarnett.plus.com> wrote: > Patrick Maupin wrote: > > On Apr 3, 11:59 am, Emile van Sebille <em...@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 -- http://mail.python.org/mailman/listinfo/python-list
