Lehman College, City University of New York

Fall 2016

For each of the following sets, state if the set is countable or uncountable. If the set is countable, explain how you can make a list of all its elements that enumerates the set.
If the set is uncountable, use the diagonalization method to show that it is not.

- The numbered subway stops in New York City.
- All odd integers (i.e. both positive and negative odd numbers).
- {w | w ends in 0} where Σ = {0,1}

(that is, all even binary numbers). - The real numbers between 0 and 1 (i.e. [0,1]).
- All possible pairs of whole numbers.