I want to show that an irrational number (let's say pi) can never have an (infinitely) repeating pattern (such as 0.12347 12347 12347 ...).

Is it possible to 'proof' (or just make it more acceptable, I don't need a 100% rigorous proof) this easily, without using too much complicated math?

Obviously the fact that no pattern has been found yet is not a convincing argument; the digits we know currently might not even have ended their first 'repeating string'.

Note; I know and accept that an irrational number cannot have an infinitely repeating string of digits (although I've never seen the proof). I just want to show (to someone else, who does not know a lot of higher math) that it is, since he won't accept the 'because it has been proven' argument.

I have read the wikipedia article on irrational numbers, and they try to explain it using long division, where a rational number n/m can be shown to always have either repeating remainders, or a zero remainder. But I don't fully understand it and I can't explain it in more accessible terms to my friend...

Thanks!