[jimktrains2]

Normal in this sense means that all the frequency of all digits approaches a uniform distribution as the length of the sample increases towards infinity. Basically if we could see "all of" π and count all the 0s, 1s 2s, 3s, &c to 9 all the counts would be equal.

[gugagore]

That on its own can't be right, because 0.12345678901234.....

According to wikipédia, you gave a definition for "simply normal", and for normal numbers the distribution of any sequence of digits is uniform. So 00, 01, ..., 99 each occur uniformally too.

[enedil]

Moreover you need to consider it with regards to all other bases than 10 too.