One of my friends made that argument that, just because a number repeats with no pattern (with certain transcendental numbers being a good example of this) then any given series of digits is guaranteed to appear

"Since Pi goes on forever and has no pattern, then

I find it difficult to either accept or reject this statement. Obviously it would take an unreasonable amount of digits for us to actually find something useful like that, but is that assumption even true in the first place?

*somewhere*within the number. For example:"Since Pi goes on forever and has no pattern, then

*somewhere*in that string of digits lies the binary code for the Microsoft Word program."I find it difficult to either accept or reject this statement. Obviously it would take an unreasonable amount of digits for us to actually find something useful like that, but is that assumption even true in the first place?

**Just because a number is transcendental and with no pattern, does that guarantee that any given string of numbers will appear somewhere in the decimal approximation, regardless of how many digits it takes to find it? Or is this just a naive assumption that isn't always true?**Furthermore, how can we know this with certainty?
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