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.
Submit your written description that your group devised.