By Sheldon Axler

Collage Algebra and Trigonometry will attract those that are looking to provide very important themes extra in-depth, higher-level insurance. this article bargains streamlined strategy observed with obtainable definitions throughout all chapters to permit for an easy-to-understand learn. collage Algebra comprises prose that's distinct, actual, and simple to learn, with trouble-free definitions of even the subjects which are normally such a lot tough for readers.

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Example 2 Write (1, 5) ∪ (3, 7] as an interval. solution The figure here shows that every number in the interval (1, 7] is either in (1, 5) or is in (3, 7] or is in both (1, 5) and (3, 7]. The figure shows that (1, 5) ∪ (3, 7] = (1, 7]. Similarly, the union of three or more sets is the collection of objects that are contained in at least one of the sets. 1 5 3 7 30 chapter 1 The Real Numbers The next example goes in the other direction, starting with a set and then writing it as a union of intervals.

Xb Finally, we conclude this subsection by recording some identities involving fractions and additive inverses: When faced with complicated expressions involving fractions that are themselves fractions, remember that division by a fraction is the same as multiplication by the fraction flipped over. 24 chapter 1 The Real Numbers Fractions and additive inverses −a a a = =− b −b b −a a = −b b a c ad − bc − = b d bd Symbolic Calculators The symbol ≈ means “approximately equal”. example 9 Over the last several decades, inexpensive electronic calculators and computers drastically changed the ease of doing calculations.

Similarly, the union of three or more sets is the collection of objects that are contained in at least one of the sets. 1 5 3 7 30 chapter 1 The Real Numbers The next example goes in the other direction, starting with a set and then writing it as a union of intervals. example 3 Write the set of nonzero real numbers as the union of two intervals. solution The set of nonzero real numbers is the union of the set of negative numbers and the set of positive numbers. In other words, the set of nonzero real numbers equals (−∞, 0) ∪ (0, ∞).