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?

Do you see a repeating pattern ih the digits of the following number, which uses only two digits:
$$0.101001000100001000001\dots?$$
