Question: The Cataloguer avoids relabeling as follows: "every entry number has a value between 0 and 1. Let's say I have a list of entry numbers and I need a new one. I just write down a decimal point, and then I go through the list. I write down a digit that is different from the first digit of the first number, and then I write down a digit that is different from the second digit of the second number, and I continue in this fashion. When I've gotten through the list, I know that I have a new number because it is different in at least one place from each number on the list."
(a) What is the set of entry numbers?
(b) How does its cardinality compare to that of N? Explain.