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The set of integers is a proper subset of the set of rational numbers.
Counting numbers are a proper subset of whole numbers which are the same as integers which are a proper subset of rational numbers.
Whole numbers are the same as integers. Whole numbers are a proper subset of rational numbers.
The Natural numbers is the set of Integers greater than 0 (ie {1, 2, 3, ...})
Mixed fractions are not integers. They consist of a whole number and a proper fraction. Integers, on the other hand, are whole numbers and their negatives, including zero, without any fractional or decimal parts.