Within a given range, the set of rational numbers is greater. Without a given range, both sets are infinite and a comparison is not very helpful.
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Yes - the set of integers is a subset of the set of rational numbers.
The set of integers includes the set of whole numbers. The set of rational numbers includes the sets of whole numbers and integers.
The set of integers is a proper subset of the set of rational numbers.
Because that is how the set of integers and the set of rational numbers are defined.
Yes, rational numbers are larger than integer because integers are part of rational numbers.