[scarmig]

My favorite irrational number is ϕ(1/10). Can you help me find (1; 2; 3; 4; 5; 6) in it in base 10? ;)

All normal numbers have the property you mentioned, and nearly all irrational numbers are normal, but there are some that are not.

[phoe-krk]

What is the phi function that you use here? If that's Euler's totient, then that does not seem to be well-defined for rational numbers...

[stephencanon]

Also, the set of “typical” numbers that we actually can prove are normal is quite small.

[scarmig]

We can prove that almost all irrational numbers are normal, which is a quite large set. It's just when we pick out a particular irrational number that we have difficulty proving normality (unless that irrational number was intentionally constructed to be normal).