Yes all counting numbers are whole numbers, but the reverse is not true (zero!)
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All counting numbers ARE (not is!) a proper subset of the set of whole numbers.
They are not. 0 (which is a whole number) is not considered a counting number(natural #).
All of the whole numbers from 10 to 99.
Yes. All prime numbers and composite numbers are positive integers, or whole counting numbers. That leaves infinitely many numbers that are neither prime nor composite. If you intended to narrow the scope of your question to the whole counting numbers or to the positive integers, then there are NO such numbers that are neither. A counting number, however large, will be either prime or composite.
-3 is a real, rational, whole integer. But then, -- All integers are real rational whole numbers. -- All whole numbers are real rational integers. -- All rational numbers are real. -- All counting numbers are real, rational, whole integers.