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.
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.