Take any set; this set and its complement are mutually exclusive. Here are some examples:
You can also take a set and its complement from a smaller universe; these would also be mutually exclusive. For example:
rational numbers and irrational numbers
Integers, Rational numbers, Real numbers and Complex numbers.
Real numbers; rational numbers; integers; and of course you can make up lots of other sets to which it belongs.
To any set that contains it! It belongs to {-22}, or {-22, sqrt(2), pi, -3/7}, or all whole numbers between -43 and 53, or multiples of 11, or composite numbers, or integers, or rational numbers, or real numbers, etc.
The one thing they have in common is that they are both so-called "real numbers". You can think of them as points on the "real number line".Both are infinitely dense, in the sense that between any two rational numbers, you can find another rational number. The same applies to the irrational numbers. Thus, there are infinitely many of each. However, the infinity of irrational numbers is a larger infinity than that of the rational numbers.
The two main DISJOINT subsets of the Real numbers are the rational numbers and the irrational numbers.
There are infinitely many subsets of real numbers. For example, {2, sqrt(27), -9.37} is one subset.
Both are subsets of the real numbers.
Rational Numbers and Irrational Numbers
10
Rational numbers.
rational numbers and irrational numbers
Only a set can have subsets, a number such as -2.38 cannot have subsets.
The set of real numbers is infinitely large, therefore it has an infinite amount of subsets. For example, {1}, {.2, 4, 800}, and {-32323, 3.14159, 32/3, 6,000,000} are all subsets of the real numbers. There are a few, important, and well studied namedsubsets of the real numbers. These include, but aren't limited to, the set of all prime numbers, square numbers, positive numbers, negative numbers, natural numbers, even numbers, odd numbers, integers, rational numbers, and irrational numbers. For more information on these, and other, specific subsets of the real numbers, follow the link below.
Are disjoint and complementary subsets of the set of real numbers.
Both rational numbers and integers are subsets of the set of real numbers.
No, but the majority of real numbers are irrational. The set of real numbers is made up from the disjoint subsets of rational numbers and irrational numbers.