Real Numbers Examples Real Numbers Examples Real Numbers are a set of all numbers ‘x’ such that ‘x’ relates to a point on the number line. The group of real numbers comprises of entire set of the rational numbers as well as the irrational numbers. To understand the real numbers examples, consider given set S = 3 / 61, 28, - √ 3, - 31, 0, 1.7, - 612, 8, - 5 / 4, √ 16, 5 ½, ∏. Now, make a list of all the constituents of the set S that belong to the set of: a) Integers, b) Whole numbers, c) Natural numbers, d) Irrational numbers, e) Irrational numbers, and, Know More About How To Solve For A Rational Number
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f) Real numbers Let us first rewrite the elements of the set S in simplified manner. S = 3 / 61, 256, - √ 3, - 31, 0, 1.7, - 612, 8, - 5 / 4, ± 4, - 11 / 2, ∏ We can clearly classify the elements of the set in the following way: 28, √ 16, - 5 ½, a) Integers: 256, - 31, 0, - 612, 8, ± 4 b) Whole numbers: 256, 8, + 4 c) Natural numbers: 0, 256, 8, + 4 d) Irrational numbers: - √ 3, ∏ e) Rational numbers: 256, - 31, 0, - 612, 8, ± 4, 3 / 61, - 5 / 4, - 11 / 2, 1.7 f) Real numbers: 3 / 61, 256, - √ 3, - 31, 0, 1.7, - 612, 8, - 5 / 4, ± 4, - 11 / 2, ∏ Thus, all the elements of the set S are indeed real numbers examples. Just about whichever number you can think of is an example of a Real Number. The only numbers that are not real are included in the set of complex numbers (or the imaginary numbers). The Real Numbers were not given an identifying name prior to the discovery of the Imaginary Numbers. They were called ‘Real’ since they were not imaginary. Read More About Solving Equations With Rational Numbers
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All numbers on the number line are the real numbers. This list consists of (but is not restricted to) positive and negative numbers, integer figures and all the rational and irrational numbers (like square and cube roots, π etc.). The set of real numbers is indicated by ‘R’. Some properties of the Real Numbers are described below: Consider three numbers X, Y and Z, which belong to the set of real numbers. 1. Commutative Property for Addition and Commutative Property for Multiplication of real numbers holds true. a. X + Y = Y + X
b. X * Y = Y * X
2. Associative Property for Addition and Associative Property for Multiplication also holds true. a. X + (Y + Z) = (X + Y) + Z
b. X * (Y * Z) = (X * Y) * Z
3. Identity Property for Addition and Identity Property for Multiplication are verifiable. a. X + 0 = 0 + X = X
b. X * 1 = 1 * X = X
4. Inverse Property for Addition and Inverse Property for Multiplication are also verifiable. a. X + (- X) = - X + X = 0
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b. X * 1/X = 1/X * X = 1
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Introduction to Rational numbers Today, I will tell you a story. Once there was a family of Natural numbers where all counting numbers used to live. One day a guest named zero visited the house and requested for a permission to stay there. All were happy; they requested the eldest member of the family Mr. infinite (∞) to grant the permission for 0. The permission was granted and the name of the house was changed to house of Whole numbers. Now, after some time negative numbers also visited the house and requested for the permission to be the part of the family. They were permitted and now the family became the family of Integers i.e. -∞ . ……..-3,-2,-1,0,1,2,3,…….∞. On seeing the family living together, some numbers which were in form of p/q, where p and q are natural numbers also asked for a permission to stay there. They were called fractions. Some fractions are 4/7, 2/5 …etc. The family of fractions also told that if you all see the denominator with you, which is not usually visible, then you will also become the part of fractions family. All the numbers started trying it and realized that they all are the part of fractions. But this was not true for negative integers. The meeting was held, in which it was decided that a name Rational number will be given to the family. A family of Rational Numbers consists of all the numbers which can be expressed in form of p/q, where p and q are integers, but q≠ 0.
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