All the Numbers - Numberphile

Caption notes

Matt Parker uses pi and Champernowne’s constant to distinguish two properties of real numbers. Pi is transcendental, yet a finite rule can approximate it to any desired precision. Normality concerns the long-run frequencies of equal-length digit strings in a given base. Concatenating the decimal representations of the positive integers constructs a base-ten normal number. The example also shows that a number can be both computable and normal.