Can anyone tell me how I could show that the following set is countable?
Natural numbers and the integers not divisible by 3?
note that the set we wish to prove is countable can be written as
now show that each of these are countable, shouldn't be that hard. then apply the theorem
you can show a set is countable by showing that there exists a bijection between the set and the natural numbers.
example, how to we know that the set of nonnegative even numbers is countable?
well, let E be the set of nonnegative even numbers.
the function given by for is one-to-one and onto.