Infinite Infinities

Infinity seems elusive. Just what size is it? There are an infinite number of numbers between zero and 1. There are also an infinite number of numbers. Is one of these sets bigger than the other?

There is an infinite number of odd numbers. There is also an infinite number of even numbers, and an infinite number of numbers divisible by five. Is the set of number divisble by five smaller than the set of odd numbers even though both are infinitely large? Is there an infinite number of infinite sets?