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The numbers used to measure real-world quantities such as length, area, volume, speed, electrical charges, probability of rain, room temperature, gross national products, growth rates, and so forth, are called real numbers. They include such number as , , , , , , , and .The basic algebraic properties of the real numbers can be expressed in terms of the two fundamental operations of addition and multiplication.
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Solution:(a) Commutative Property for addition (b) Associative Property for addition (c) Commutative Property for multiplication (d) Distributive Property (e) Additive Inverse Property (f) Multiplicative Identity Property (g) Multiplicative Inverse Property
Many of the important properties of the real numbers can be derived as results of the basic properties, although we shall not do so here. Among the more important
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