How can pi have infinite number of digits and never repeat them? I am very confused about this matter, even if I searched google about this already. Please show me how this is determined and/or at least explain to me.
First, I saw this "Infinite Monkey Theorem" that says given infinite number of tries, a monkey could write a play of Shakespeare exactly. If so, why not "given infinite number of digits of pi, a pattern will form?"
Second, "if the digits are finite, then I can write this number as the ratio of two integers." And I found out that pi is the ratio of the circumference and diameter of a circle. If it this is so, then how come pi is proved to be infinite?

For the first question: I think you are confusing things here. The Infinite Monkey Theorem does state that, but it doesn't state that the monkey should keep writing the same play of Shakespeare's over and over again in some particular pattern. The same thing goes for $\pi$.
For the second question: the thing is that neither the circumference nor the diameter need be integers. 
