Chapter 2.7, Problem 47MS

Is y irrational? You decide to create the digits of a decimal number y between 0 and 1 using the function $f(n)=3n+1.$ Here’s your system. Compute f(1) and put the result as the first digit of y to the right of the decimal point. Compute f(2) and put the result as the second digit of y. Compute f(3) and put the result as the third and fourth digits of y. Compute f(4) and put the result as the fifth and sixth digits of y. And so on. What’s the tenth digit of y? Do you think y is irrational? Why or why not?