To describe all the sets and subsets that 2/3 belongs to, we first need to understand the concept of sets and subsets.
A set is a collection of distinct elements. It can contain any type of object or elements, such as numbers, letters, or other sets. For example, a set of even numbers could be {2, 4, 6, 8, ...}.
A subset is a set that contains only elements from another set, called the parent set. In other words, every element in a subset must also be present in the parent set. For example, if we have a parent set of {1, 2, 3, 4}, some possible subsets are {1, 2}, {3, 4}, and {1, 4}, among others.
Now, let's determine the sets and subsets that 2/3 belongs to.
1. Set of Real Numbers: 2/3 is a real number, so it belongs to the set of real numbers. This set includes all rational and irrational numbers.
2. Set of Rational Numbers: Since 2/3 can be expressed as a fraction, it belongs to the set of rational numbers. Rational numbers are numbers that can be expressed as a ratio of two integers (with a non-zero denominator).
3. Set of Fractions: As 2/3 is a fraction itself, it belongs to the set of fractions. Fractions represent a part of a whole and can be written in the form a/b, where a and b are integers and b is not zero.
4. Subset of Positive Rational Numbers: Since 2/3 is a positive fraction, it is a subset of the positive rational numbers. This subset includes all positive fractions expressed in the form a/b, where both a and b are positive integers.
5. Subset of Proper Fractions: A proper fraction is a fraction where the numerator is smaller than the denominator. Since 2/3 is a proper fraction, it belongs to this subset.
These are some examples of sets and subsets that 2/3 belongs to. However, keep in mind that there are many more sets and subsets that 2/3 could be a part of depending on the context and specific mathematical definitions being used.