describe all the sets and subsets the number 2/3 belongs to
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.
To describe all the sets and subsets to which the number 2/3 belongs, we need to consider various mathematical sets. Here are some possible sets and subsets:
1. Real Numbers (R): The number 2/3 belongs to the set of real numbers, which includes all rational and irrational numbers.
2. Rational Numbers (Q): The number 2/3 belongs to the set of rational numbers since it can be expressed as a fraction. Rational numbers include integers, fractions, and terminating or repeating decimals.
3. Proper Subset of Q: The number 2/3 belongs to the proper subset of Q, which is the set of rational numbers excluding the integer set (Z).
4. Proper Subset of R: The number 2/3 belongs to the proper subset of R, which includes all real numbers except for irrational numbers.
5. Proper Subset of Positive Rational Numbers: The number 2/3 belongs to the proper subset of positive rational numbers (Q+), which includes all positive fractions and does not include zero or negative fractions.
6. Proper Subset of Positive Real Numbers: The number 2/3 belongs to the proper subset of positive real numbers (R+), which includes all positive real numbers, excluding zero and negative numbers.
It's important to note that these are just a few examples of sets and subsets to which the number 2/3 belongs. There are many other sets and subsets that can be defined based on different mathematical contexts or requirements.
To determine the sets and subsets to which the number 2/3 belongs, we need to consider the mathematical hierarchy of sets.
1. Universal Set (U): The universal set is the collection of all possible elements. Without more context or specific instructions, let's assume we are working with the set of real numbers (denoted by R), which contains all possible real numbers.
2. Rational Numbers (Q): Rational numbers are those that can be expressed as a ratio of two integers, where the denominator is not zero. The number 2/3 is a rational number because it can be written as the fraction 2/3.
3. Proper Subset of Q: The number 2/3 belongs to the proper subset of Q, which includes only a portion of the rational numbers. Since 2/3 is a rational number, it is automatically part of this subset.
4. Integers (Z): Integers are whole numbers, including both positive and negative values, as well as zero. The number 2/3 is not an integer since it is a fraction between 0 and 1, inclusive.
5. Natural Numbers (N): Natural numbers are counting numbers, including zero but not negative numbers. The number 2/3 is not a natural number because it is a fraction between 0 and 1, exclusive.
To summarize, the number 2/3 belongs to the sets of Rational Numbers (Q) and the Proper Subset of Q. It does not belong to the sets of Integers (Z) or Natural Numbers (N).