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

Integers are whole numbers.

mixed number are whole numbers plus fractions ... that when simplified, become improper fractions

2 1/2 = 5/2 ... this is not an integer or a whole number

3 1/4 = 13/4 ... same here ... not an integer or a whole number

4 1/3 = 13/3 ... not an integer or a whole number