Is there a proof that $\pi$ is an irrational number? Most math texts claim that $\pi$ is an irrational number. However, I'm having a little bit of trouble understanding that.
Since nobody has calculated all of the digits of $\pi$, how can we know that either:


*

*one of the digits repeats (as in $\frac{10}{3}$)

*the number eventually terminates



Note: Please be very descriptive in your answers... I don't have anything beyond high school math.

There are quite a number of proofs on Wikipedia. Not sure how accessible you will find them, though -- feel free to ask about one of them that you might be able to understand.
