Well, this is a standard mathematical result. Basically there is a set called Q of all rational numbers, which means all numbers that can be written in the form n/m.

However, you would think that this is all you need to express all the numbers forgetting complex numbers. However, it is not.

Consider this.

A dice 10 sided dice has 0 to 9 written on one of its side. Just like a six sided dice, but more sides. Now, n/m means that it has a repeating pattern. However, consider rolling the dice, is it likely it will have a pattern or more likely it will not have a pattarn?

Well, it very much more likely it will not have a repeating pattern meaning it can't be written in the form n/m.

Now a very improtant result in set theory is that Q can be counted, i.e. it can have one to one correspondence with the natural numbers, so basically you can write first of Q for example 1-1 then 1/2-2 then 1/3-3. Now, you can count Q, however you cannot count the real numbers or R. This shows to things, that infinity can come in two sizes and that there is more randomness or unrepeating patterns in the number line then there is patterns.

Anyway, there is alot of randomness in the world and espically in set theory.

I was the movie Pi, which is rubbish. Basically, at the beginning he said there are patterns, however I think he should have pointed out the lack of patterns in nature.

P.S. This is why mathematics is soo cool.