Why a mixed number is not in the set of integers or whole numbers

A mixed number can be rewritten as the quotient of two numbers. For instance, "1 and 1/4" = 5/4. 5 is not a multiple of 4 and therefore 5/4 is neither an integer nor a whole number. By definition, a mixed number has a nonzero remainder. Both integers and whole numbers have no remainder by definition, so it is impossible for a mixed number to be either.