describe all the sets and subsets the number 2/3 belongs to

Answer 1

The number 2/3 belongs to several sets and subsets:

1. Rational Numbers: The number 2/3 is a rational number, which means it can be expressed as a fraction of two integers.

2. Real Numbers: The set of real numbers includes rational numbers like 2/3, as well as irrational numbers such as √2 or π.

3. Positive Rational Numbers: 2/3 is a positive rational number as it is greater than zero and can be expressed as a fraction with a positive numerator and denominator.

4. Proper Rational Numbers: A proper rational number is a fraction where the absolute value of the numerator is less than the absolute value of the denominator. Since |2| < |3|, 2/3 is a proper rational number.

5. Prime Rational Numbers: A prime rational number is a fraction that cannot be simplified further. As 2 and 3 are both prime numbers and 2/3 cannot be reduced any further, it is a prime rational number.

6. Integers: Although 2/3 is not an integer, it can be expressed as a fraction where the numerator is an integer (2) and the denominator is a nonzero integer (3).

7. Whole Numbers: Since 2/3 is not a whole number, it does not belong to this set.

8. Natural Numbers: 2/3 is not a natural number as it is not a positive integer.

9. Nonnegative Rational Numbers: 2/3 is a nonnegative rational number because it is greater than or equal to zero.

These are all the important sets and subsets to which the number 2/3 belongs.