Abstract
As we all know, one of the important properties of real numbers is comparability. We can compare two distinct real numbers and say that one is smaller or larger than the other. There is an inherent ordering < on the real number system ℝ which helps us to compare two real numbers. The basic properties of this ordering on ℝ are:
(i) Given any two real numbers a and b, one and only one of the following three relations is true:
a < b or a = b or a > b;
(law of trichotomy.)
(ii) a > 0 and b > 0 imply a + b > 0;
(iii) a > 0 and b > 0 imply ab > 0.
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© 2018 Springer Nature Singapore Pte Ltd. 2018 and Hindustan Book Agency
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Venkatachala, B.J. (2018). Some basic inequalities. In: Inequalities. Texts and Readings in Mathematics, vol 49. Springer, Singapore. https://doi.org/10.1007/978-981-10-8732-5_1
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DOI: https://doi.org/10.1007/978-981-10-8732-5_1
Publisher Name: Springer, Singapore
Online ISBN: 978-981-10-8732-5
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