A real number x in R is computable if there is a computable function f : Z $->\{0,...,9\}$ that gives the ith digit

of x$,$ that is: f $($i$)=$ ith digit of x for all i $($negative digits are the digits after the decimal point$).$ Intuitively, if

a real number is computable then there is an algorithm to calculate an arbitrary approximation of it $($this is

true for all constants you$$re familiar with, including $\backslash$pi and e$).$

Show that there are uncomputable real numbers.