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Real Numbers Definition Real Numbers Definition

In general terms, real numbers are those numbers which do not considered as an imaginary numbers. In the mathematics real number plays an important role to solve various types of problems. In the real number we consider general type of numbers like 1 to 9, 12.34, -16, 6/7, etc. According to real numbers definition, we can take any type of numbers which may be positive or negative, natural number, whole numbers, fractional numbers, integers and number either a large or small all are considered as real numbers. In the sum of real number definition, I want to say that the real number is a number which represent any particular or fix amount of quantity. Know More About Free Tutor


History of Real Numbers The history of real numbers starts with two major periods - first one is classical Greek mathematics. The classical Greek mathematics emerged as a deductive science. The second one is the rigorization and the formalization of mathematics which developed in the 19th century. But in that time, there was lack of knowledge and weakness to understand the real number, and because of this reason the mathematician were unable to expand their ideas. The natural numbers were developed or understood by Greek mathematicians. They also developed an idea of how we call the whole number ratios, rational and real numbers. But now a day’s these systems are not treated as they were known in that time. When any number system has been developed to modern standards, it is necessary to develop that number system in the Method of Exhaustion.

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The real numbers and the integral calculus demonstrate the Method of Exhaustion. But this was not subsequently matched with formalization of mathematics in the 19th century. Mathematicians in the 19th century further analyzed these ideas and then improved the ideas on which this field is based. The Indian and Chinese mathematicians developed the science of the acceptance of zero, negative, real, integral and fractional numbers which were later on used by Arabic mathematicians in middle ages and they were first to treat irrational numbers as algebraic objects. This was made possible by the development of algebra. Arabic mathematicians improved the concepts of numbers and magnitude into the real numbers. Egyptian mathematician Abu Kamil Shuja ibn Aslam was the first person who accepted irrational numbers as solution of quadratic equations or as coefficients in equations generally in the form of square roots, cube roots and so on. Around 500 BC, Greek mathematicians realized the need for irrational numbers particularly the square root of two. In this way the real number system was developed.


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Real Numbers Definition  

In the real number we consider general type of numbers like 1 to 9, 12.34, -16, 6/7, etc. According to real numbers definition, we can take...

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