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Chapter 4 Equations

Chapter 4 Equations. In this chapter we discuss general ideas relating to equations and their solutions. Uses of Equations. To express a relationship among numbers or variables To express one variable in terms of another To define a function To describe a graph (curve or surface)

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Chapter 4 Equations

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  1. Chapter 4 Equations In this chapter we discuss general ideas relating to equations and their solutions.

  2. Uses of Equations • To express a relationship among numbers or variables • To express one variable in terms of another • To define a function • To describe a graph (curve or surface) • To provide information about when a particular quantity is maximized or minimized

  3. 4.1 The Concept of Equation • An equation or equality is a sentence of the form A = B, where A and B may be numbers, algebraic expressions, sets, etc. • “Equality in a given mathematical context is usually defined in terms of equality in a more primitive context where its meaning has already been defined or is taken as understood.” • “Ultimately the equality of most mathematical objects can be traced back to equality of sets.”

  4. Definition of set equality • Sets A and B are equal if and only if they contain exactly the same elements: each element of A is also an element of B and each element of B is also an element of A

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