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The derived set of a set of rational numbers is the set of all limit points of the original set. In other words, it includes all real numbers that can be approached arbitrarily closely by elements of the set. Since the rational numbers are dense in the real numbers, the derived set of a set of rational numbers is the set of all real numbers.
define or describe each set of real numbers?
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Because adding any set of real numbers together will result in another real number.
It is the set of Real numbers.