The basic sets that make up the real number system are:
1. Natural numbers (N)
2. Whole numbers (W)
3. Integers (Z)
4. Rational numbers (Q)
5. Irrational numbers (I)
6. Real numbers (R)
What are the natural algebraic operations endowed in each of the sets mentioned above
1. Natural numbers (N): The algebraic operations that can be performed with natural numbers are addition, subtraction, multiplication, and division (although division may result in a non-natural number).
2. Whole numbers (W): The algebraic operations that can be performed with whole numbers are the same as those for natural numbers - addition, subtraction, multiplication, and division (with the caveat that division may result in a non-whole number).
3. Integers (Z): In addition to the basic algebraic operations of addition, subtraction, multiplication, and division, integers also include the operation of finding the absolute value of a number.
4. Rational numbers (Q): The algebraic operations that can be performed with rational numbers include addition, subtraction, multiplication, division, and exponentiation.
5. Irrational numbers (I): Although irrational numbers cannot be expressed as a fraction, they can still participate in the basic algebraic operations of addition, subtraction, multiplication, and division.
6. Real numbers (R): Real numbers include all the aforementioned sets (natural numbers, whole numbers, integers, rational numbers, and irrational numbers) and can participate in all algebraic operations mentioned above.