>>13189736Your statement as it is written is false: the string of infinitely repeated 0s doesn't contain the pattern "1".
Assuming that you're talking about a random infinite string where all characters are equally likely to appear at any given position: let s be a finite string of n characters, since the alphabet is finite there is a non-zero probability that a string of n random characters is equal to s. Now if you read your string n characters at a time, since they are random and independent you are basically generating random strings of length n an infinite number of times, therefore s will be in the infinite string with probability 1 (100%).
