Rational numbers encompass integers and fractions, possess properties ensuring closure under basic arithmetic operations, and are defined by the completeness axiom in real numbers.
Rational numbers are numbers that can be expressed as a ratio of two integers, such as 2/1 and 3/4. They include integers and fractions. One of the important properties of rational numbers is that they can be expressed as terminating or repeating decimals, such as 0.5 or 0.3333...
Another significant property of rational numbers is that when multiplied, divided, added, or subtracted, they always result in a rational number. For example, multiplying 2/3 by 3/4 yields 1/2, which is still a rational number.
Completeness is a critical concept related to rational numbers. The completeness axiom of the real numbers ensures that for any non-empty subset of rational numbers that is bounded above, there exists a least upper bound.
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