When we hear the word number, symbols like 1,,¼, π (area enclosed by a unit circle), ι (symbol for ), ε (infinitesimal), ω (ordinal infinity), ℵ (cardinal infinity), …. appear in our mind. But not all numbers are computable:

A computable number [is] one for which there is a Turing machine which, given

non its initial tape, terminates with thenthdigit of that number [encoded on its tape].

In other words, a real number is called computable if there is an algorithm which, given *n*, returns the first *n* digits of the number. This is equivalent to the existence of a program that enumerates the digits of the real number. For example, π is a computable number (why? see here).

Using Cantor’s diagonal argument on a list of all computable numbers, we get a non-computable number (here is the discussion). For example, a sum of series of real numbers called Chaitin’s constant, denoted by Ω, is a non-computable number (why? see here).

**Fun fact**: We don’t know whether π is a normal number or not (though we want it to be a normal number), but Ω is known to be a normal number (just like the Mahler’s Number discussed here).