Re: crazy, man... crazy

--- In crazy_music@y..., "X. J. Scott" <xjscott@e...> wrote:

/crazy_music/topicId_65.html#74

> > [monz:]
> >
> > If you multiply the number by any integer denominator and
> > you can't get rid of the decimal in the numerator, it's
> > irrational.
>
> Not following this, I think you meant to say something
> else.

Nope - that's what I meant. Illustration: pi

pi * 1 = 3.141592654
pi * 2 = 6.283185307
pi * 3 = 9.424777961
pi * 4 = 12.56637061
pi * 5 = 15.70796327
pi * 6 = 18.84955592
pi * 7 = 21.99114858
pi * 8 = 25.13274123

The first thing you notice is that pi is just a little over 3.

The next product that is nearly an integer is pi*7, which
is just a hair under 22. In times and places without digital
calculators, 22/7 was and is a very commonly used approximation
to pi.

But it's *still* an approximation. If one goes on multiplying
pi by the series of integers forever, the product will never
be an exact integer.

That's what I meant. It's rather clumsy, and one of the
mathematicians here could state it a lot more elegantly.
... I suppose Graham has already done it well enough.

>
> Also, when Graham said "A rational number is a fraction
> composed of two integers" I think he meant "A rational
> number is a fraction composed of whole numbers", since 0/0
> and 1/0 are not rational.

Correct, and an important observation. Right, Graham?...

-monz
http://www.monz.org
"All roads lead to n^0"