The Singleton & Empty Set Video Lecture | Mathematics for GRE Paper II

Ans. The Singleton pattern is a design pattern that restricts the instantiation of a class to a single object. It ensures that only one instance of the class exists throughout the application and provides a global point of access to that instance. This pattern is commonly used in scenarios where a single instance of a class needs to coordinate actions across the system.

Ans. No, a Singleton class can have only one instance. The purpose of the Singleton pattern is to restrict the instantiation to a single object. If multiple instances were allowed, it would defeat the purpose of the pattern.

Ans. In Java, the Singleton pattern can be implemented by creating a private constructor, a private static instance of the class, and a public static method that returns the instance. The static method checks if the instance is null and creates a new instance if it doesn't exist, or returns the existing instance otherwise. This ensures that only one instance of the class is created and accessed.

Ans. The advantages of using the Singleton pattern include: - Global access to the instance: It provides a centralized point of access to the instance, allowing other parts of the code to easily use and interact with it. - Resource sharing: Since there is only one instance, it can be used to share resources efficiently across different parts of the application. - Lazy initialization: The instance is created only when it is first needed, reducing memory usage and improving performance. - Thread safety: The Singleton pattern can be implemented to handle concurrent access, ensuring that only one thread can create and access the instance at a time.

Ans. In mathematics, the empty set, often denoted by the symbol Ø or {}, is a set with no elements. It is a unique set that represents the absence of any elements. The empty set is an important concept in set theory and is used as a foundation for various mathematical operations and proofs.