Definition of Real Numbers Definition of Real Numbers A Real Number in mathematics is basically a value which is used to represent a quantity which is not an imaginary value. A real number can be any integer value either positive or negative. Real numbers involves almost all the integers and rational and irrational numbers. Rational numbers are the numbers which are represented as a fraction such ½, 5/3 etc. Irrational numbers are the numbers which are represented by a decimal point such 3.1413563…etc. Real numbers generally includes both the rational and irrational numbers. If a real number is consisting of a decimal point then it is called a floating point number. Real numbers may consist of a number of points on an infinitely long line; this line is known as number line. On number line or real line the integer values corresponding to the points are distributed with equal spacing among them. Numbers such 1, 2, 14.32, -0.5, 2/5, ¼ etc all are the real numbers. These numbers can be positive or negative, large or small numbers. These numbers are real numbers because these are not consisting of the imaginary number. An imaginary number includes a symbol iota (i) such a – ib, a + ib etc. A real number can be rational or irrational, algebraic or transcendental, positive or negative or zero. So real numbers are basically used for measuring the continuous quantities. These numbers can also be thought as the value which expresses a quantity along with a continuous line. So the real number definition can be given as....... Know More About :- Difference Definition
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A system of real number is a set of (r, +, *, <) where r denotes the set of real numbers which have usual properties of addition, multiplication and of total ordering.The real number set r is basically a field which can perform addition and multiplication. Similarly real number set r is ordered i.e. numbers in set r can be total ordered by using <. Total ordering can be done by ≤ or ≥ operators i.e. let there are 3 real numbers sam l, m, n then to order them: a. if l ≥ m then l + n ≥ m + n b.
if l ≥ 0 and m ≥ 0 then l*m ≥ 0.
Now here are some general properties of real numbers: Real numbers are used in various problems of mathematics. Let l, m, n are real numbers then § Associative property of addition: l + (m + n) = (l + m) + n § Commutative property of addition: l + m = m + l § Associative property of multiplication: l * (m * n) = (l * m) * n § Commutative property of multiplication: l * m = m * l § Distributive: l. (m + n) = l. m + l. n § Identity property of addition: l + 0 = l § Identity property of multiplication: l * 1 = l § Nero property: l * 0 = 0 § Inverse property of addition: l + (-l) = 0 § Inverse property of multiplication: l * (1/l) = 1 So today we learnt the definition of real numbers, Read More About :- Algebra Expression
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