... it should be noted that the sequence of digits to the right of the decimal point in their infinite expansions is effectively random.This is only true with probablity one. There are irrational, verily, even transcendental, numbers with non-random decimal expansions.
.10100100010000100000....
An example which no polynomially bound statistical test can prove to be non-random:
1101110010111011110001001101010111100110111101111...
Each of the above has an obcious construction rule.
Yes, and I almost included
0.123456789101112...
and
0.101001000100001000001...
in an earlier post, but didn't. I've got to remember that there are readers here who know what expressions like 'except on a set of measure zero' mean.
We're out here holding up the tails of the bell curve. Without us, it would be exp(-x**3).