Implicitly defining a number via it’s decimal form typically relies on their being a pattern to follow after the ellipsis. You can define a different number with twos in it, but if you put an ellipsis at the end you’re implying there’s a different pattern to follow for the rest of the decimal expansion, hence your number is not the same number as the one without twos in it.
Right and the point of defining this number as a non-repeating infinite sequence of 0s and 1s is just to show that non-repetition of digits alone is not sufficient to say a number contains all finite sequences.
That trivial point is not the one we (you and me) are contending.
The issue is that OP hasn’t actually defined the sequence, just given some properties (which does not lead to any definition or determination of the location of the number/s on the number line, by itself). Assuming that he has defined it, doesn’t change anything as any other commentator can assume something different, which consistent with OP’s post.
Implicitly defining a number via it’s decimal form typically relies on their being a pattern to follow after the ellipsis. You can define a different number with twos in it, but if you put an ellipsis at the end you’re implying there’s a different pattern to follow for the rest of the decimal expansion, hence your number is not the same number as the one without twos in it.
assumption ≠ definition
Math kind of relies on assumptions, you really can’t get anywhere in math without an assumption at the beginning of your thought process.
Obviously. But still maths avoids stuff like “I assume the answer is X. QED.”
Right and the point of defining this number as a non-repeating infinite sequence of 0s and 1s is just to show that non-repetition of digits alone is not sufficient to say a number contains all finite sequences.
That trivial point is not the one we (you and me) are contending.
The issue is that OP hasn’t actually defined the sequence, just given some properties (which does not lead to any definition or determination of the location of the number/s on the number line, by itself). Assuming that he has defined it, doesn’t change anything as any other commentator can assume something different, which consistent with OP’s post.