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Can a subset of infinite set be infinite?
Yes. For example, the set of odd natural numbers is a infinite subset of the set of integers.
How integers and whole numbers the same?
Each integer is a whole number and each whole number is an integer. So the set of all integers is the same as the set of all whole numbers. By the equivalence of sets, integers and whole numbers are the same.
Why the set of mixed numbers is not a subset of the set of integers?
Mixed numbers and integers are different things.
What is a set of numbers that includes 1 but not zero?
The set of positive integers contains 1 but not zero. Within the set of integers, there is the subset of positive integers, the subset of negative integers and the subset with a single element in it - zero. There are a zillion other sets that could be specified that meet the conditions set down in the question. The one cited is an easy one.
Can the set of mixed numbers is the union of the set of integers and the set of fraction?
No, the set of mixed numbers is a subset of the set of rational numbers. For example the mixed number 1 ¼ is the same as the improper fraction 5/4 [a rational number]. Note that it is a subset, because integers are also rational numbers, but a mixed number will not be an integer. Also, any fraction between 0 and 1 will not be a mixed number.
