Sets - null, singleton, universal set, finite infinite sets, countable uncountable sets
Channel: Binary Cave
Date: 2020-04-24

Now let's understand few more definitions related to sets:
 1. Empty or null set:- A set that contains no element is called the empty set or the null set and is denoted by { } or ∅.
 e.g., the set  S of all positive integers that are greater than their square is a null set. There is not positive integer which is greater than its square, Hence no item belong to this set. Hence is a null or empty set.
 S  = { }
 2. Singleton set:-  A set with single item is called a singleton set. 
 e.g., the set S of prime numbers less than 2. Since there is a single prime number 1 that is less than 2, hence it is a singleton set.
 S = {1}
 3. Universal set (U): A universal set denoted by U contains all elements under consideration. The universal set varies depending on which objects are of interest. For example, if we a student set under consideration, then universal set represents all possible students. Similarly, if numbers are under consideration, then universal set U represents all possible numbers.
 4. Cardinality of a set: The number of elements in a set is called its cardinality and is denoted by | |. e.g., 
 Let A = {1,3,5,7} be a set of some prime numbers then, its cardinality is 5 and is written as:
 |A| = 5.