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Yes, both rational and irrational numbers are part of the set of real numbers.
The real numbers are defined as the set of all numbers that can be represented as a decimal expansion, either finite or infinite. This includes both rational and irrational numbers.
Rational numbers are those numbers that can be expressed as the ratio of two integers, such as 1/2, 3/4, -5/6, etc. They can also be expressed as finite decimal expansions or repeating decimals. For example, 1/4 can be written as 0.25, and 1/3 can be written as 0.3333…, where the digit 3 repeats indefinitely.
Irrational numbers, on the other hand, cannot be expressed as the ratio of two integers. They are numbers that have decimal expansions that neither terminate nor repeat, such as the square root of 2 (approximately 1.41421356…) or pi (approximately 3.14159265…).
Therefore, both rational and irrational numbers are part of the set of real numbers.