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An Introduction to Basic Set Theory

Restricted Functions

Explore the concept of restricted functions in set theory by examining how functions can be limited to subsets of their domains. Understand practical examples including restrictions on integer and real number functions, and the importance of domain considerations for defining valid restricted functions.

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What is a restricted function?

It is sometimes useful to look at a function that focuses on a subset of the domain. Let’s consider f:A→Bf: A\to B, where the domain set is AA and ff is a function from AA to BB. If we take CC—a subset of AA—then the restricted function f∣C:C→Bf{\mid}_C : C\to B provides a function from CC to BB. We can recognize it as restricting ff to CC ...