Can anyone tell me how I could show that the following set is countable?
Natural numbers and the real numbers with decimal representations consisting of all 1's?
Here's a hint: You can identify such a number with the couple where is the number of 1's on the left, and the number of 1's on the right. (Actually, you should probably also consider as a possibility.) From there, it should be clear whether the set is countable or uncountable.