Question

what is real number? explain the completeness property​

Answer 1

Answer:

The Completeness Property of The Real Numbers: Every nonempty subset of the real numbers that is bounded above has a supremum in . The Completeness Property is also often called the "Least Upper Bound Property". ... Theorem 1: Every nonempty subset of the real numbers that is bounded below has an infimum in .

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Answer 2

Answer:

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion). The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2 (1.41421356..., the square root of 2, an irrational algebraic number). Included within the irrationals are the real transcendental numbers, such as π (3.14159265...).In addition to measuring distance, real numbers can be used to measure quantities such as time, mass, energy, velocity, and many more. The set of real numbers is denoted using the symbol R or {\displaystyle \mathbb {R} }\mathbb {R} and is sometimes called "the reals".

Real numbers are the numbers which include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.Zero is considered as both a real and an imaginary number. As we know, imaginary numbers are the square root of non-positive real numbers. And since 0 is also a non-positive number, therefore it fulfils the criteria of the imaginary number. Whereas 0 is also a rational number, which is defined in a number line and hence a real number.