Interactive Real Analysis - part of MathCS.org

• Real Analysis
• 1. Sets and Relations
• 1.1. Notation and Set Theory
• 1.2. Relations and Functions
• 1.3. Equivalence Relations and Classes
• 1.4. Natural Numbers, Integers, and Rational Numbers
• 2. Infinity and Induction
• 3. Sequences of Numbers
• 4. Series of Numbers
• 5. Topology
• 6. Limits, Continuity, and Differentiation
• 7. The Integral
• 8. Sequences of Functions
• 9. Historical Tidbits
• Java Tools

Definition 1.2.2: Function, Domain, and Range

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Let A and B be two sets. A function f from A to B is a relation between A and B such that for each a A there is one and only one associated b B. The set A is called the domain of the function, B is called its range.

Often a function is denoted by y = f(x) or simply f(x), indicating the relation { (x,f(x)) }.

Context

Note: James Cranston (cranstonjames123@gmail.com)) pointed out that occasionally the term codomain is used instead of range, in which case the term range denotes the image of the domain under the function f and is a subset of the codomin. We will, however, stick with our defintion of range as the set containing all values f(a) and possibly more elements; we won't use codomain at all.