Definitions from the Web
Term: Indicator Function
Description: The indicator function, also known as a characteristic function or a boolean function, is a mathematical function that indicates whether a given element belongs to a set or satisfies a specific condition. It is commonly used in various branches of mathematics and computer science.
Senses and Usages:
- Mathematics:
- Sense: In mathematics, the indicator function is a function defined on a set that takes the value 1 if the element belongs to the set and 0 otherwise.
- Usage: The indicator function is extensively used in set theory, measure theory, and probability theory to define characteristic functions for various sets and events.
- Sample Sentence: The indicator function of the set A, denoted as 𝟙A(x), equals 1 if x belongs to A, and 0 otherwise.
- Computer Science:
- Sense: In computer science, an indicator function represents the state or condition of a certain process or system.
- Usage: Indicator functions are commonly used in algorithms, programming languages, and data structures to flag or track specific conditions or properties.
- Sample Sentence: The indicator function for a specific process keeps track of whether it is currently running (1) or stopped (0).
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