a) Denote by $S(n)$ the sum of digits of a positive integer $n$. After the decimal point, we write one after the other the numbers $S(1),S(2),...$. Show that the number obtained is irrational. b) Denote by $P(n)$ the product of digits of a positive integer $n$. After the decimal point, we write one after the other the numbers $P(1),P(2),...$. Show that the number obtained is irrational.