Surprisingly, no. For example, even though every whole number is also a rational number, mathematicians would say the size (or more accurately, the cardinality)

Surprisingly, no. For example, even though every whole number is also a rational number, mathematicians would say the size (or more accurately, the cardinality) of the set of whole numbers is the same as that of the set of rational numbers. I'm personally a fan of the Infinite Hotel Paradox as an introduction to the subject.