Observation: There are infinitely many COUNTING NUMBERS and infinitely many FRACTIONS.
Question: Which infinity is greater?
Answer: Even though there are infinitely many fractions between each pair of consecutive counting numbers, the arrows in the diagram below show how to match the red counting numbers with the blue fractions.
So the infinities are the same size. There are just as many counting numbers as there are fractions!
Last Updated February 7, 2022