(4 points) Suppose you take the line below, cut it in half, and then take the left piece and cut it in half, and then take the leftmost piece and cut it in half, and so on, without ever stopping. How many different pieces of the line would you have? Does the set of all pieces have the same cardinality as the set of all natural numbers? Justify your answer. (4 points) First, consider the following innite collection of real numbers. Describe in your own words how these numbers are constructed (that is, describe the procedure for generating this list of numbers). Then, using Cantor's diagonalization argument, nd a number that is not on the list. Give at least the rst 10 digits of the number and explain how to nd the rest. How do you know that your number is not on the list? U.123456789101112131415161718 . . . U.2468101214161820222426283032 . . . 0.369121518212427303336394245 . . . U.4812162024283236404448525660 . . . 0.510152025303540455055606570