Normality is not necessary. Counter-counter example is the digits of pi in groups of 1, 2, 3... with strings of zeros in between:
3.0140015900026530000....
this number is obviously nor normal since 0 occurs with greater frequency than any other digit. But if pi is normal, then this sequence contains all finite sequences too.
Comments
Normality is not necessary. Counter-counter example is the digits of pi in groups of 1, 2, 3... with strings of zeros in between:
this number is obviously nor normal since 0 occurs with greater frequency than any other digit. But if pi is normal, then this sequence contains all finite sequences too.