Naked Science Forum

General Science => General Science => Topic started by: Felix Nielsen on 26/07/2008 15:13:32

Title: Is the lack of pattern in irrational numbers a pattern in itself?
Post by: Felix Nielsen on 26/07/2008 15:13:32

Felix Nielsen asked the Naked Scientists:

I have a great interest in maths and often have questions to which I cannot find an answer.

Most of the questions is too complex and is not suitable for your
programme (http://www.thenakedscientists.com/HTML/podcasts/), but one of them might be.

Almost any number can be be written as a fraction, these we call natural, whole or rational numbers. These numbers all have got patterns. fx. 10/11 0.90909090909.... and you clearly see the pattern.
However, a small group of numbers remains, those with no patterns, and we call them irrational numbers.  Numbers like Pi, the square root of two are irrational numbers, as they have no patterns.
(I realize that this was quite a long introduction and I of course expect you to edit it as you see fit)

Now, the question is:
Could the absent pattern in such numbers be a pattern in it self? Have anyone done research in this area? Has a conclusion been made?

Thanks

What do you think?

Title: Is the lack of pattern in irrational numbers a pattern in itself?
Post by: lyner on 26/07/2008 17:14:02

Actually, Pi and e are not just irrational numbers - they are transcendental numbers. They are not the roots of any algebraic equation. Numbers - like root 2, root 3 etc are irrational, they are the roots of 'simple' equations.
It is a moot point s to whether there are, in fact, more rational than irrational numbers. Just 'cos we can think of more doesn't mean there are more.
Pi, e and others, come from more complex equations, involving trigonometry, integration, logarithms, etc.

Title: Is the lack of pattern in irrational numbers a pattern in itself?
Post by: graham.d on 26/07/2008 17:34:52

I think there is a quite simple proof that shows there are more irrational numbers than rational numbers. I was shown it many years ago but don't remember it. It will be on the web somewhere.

Title: Is the lack of pattern in irrational numbers a pattern in itself?
Post by: graham.d on 26/07/2008 18:00:54

Cantor's diagonalization argument maybe...

No time to check right now.

Title: Is the lack of pattern in irrational numbers a pattern in itself?
Post by: lightarrow on 26/07/2008 22:49:15

Quote from: graham.d on 26/07/2008 18:00:54

Cantor's diagonalization argument maybe...

No time to check right now.

Yes, rational numbers are numerable, while irrationals not.