Quote Originally Posted by niveK
Quote Originally Posted by niffweed17
no. this is very important: what i said applies only to finite sequences of numbers. what you are describing here applies to an infinite sequence of numbers. exactly one infinite sequence of numbers could ever occur in an irrational number or an infinite sequence of randomly selected digits (ill call this a number as opposed to a sequence to attempt to reduce ambiguity), namely the sequence of numbers you started with. no other infinite sequence could ever apply, because there would always be a digit in the number which is not included in the sequence. the only exception is the sequence of numbers which is precisely defined by the number.

as an analogy, the only number which is exactly equal to pi is pi. the number 3.2415926... (converging infinitely to some value with the remaining digits equal to that of pi) is not equal to pi since it has one error, even though the remainder of its digits are identical to those of pi. no matter how many digits that conform to a specified infinite sequence, there will always be at least one digit that is not part of the sequence, unless the sequence itself is being defined.
No, I understood the "finite" limitation on the sequences. I should have specified that in the last sentence of that paragraph.
ok, but the "thought experiment" which you described was not finite and didn't work because it was not finite, and as a result of this was internally inconsistent.