Searching definitions of Set, Null Set, Singleton Set, and Finite Set with Examples, here you will get everything
So, In this article, you will get all the definitions of the Set related terms along will their perfect examples. You can write these definitions and the examples too in your homework, classwork, or exams. No teacher will mark it as wrong. So, let’s get into the main part of the article.
What is a Set?
A Set is a
collection of distinct objects, which can be anything from numbers to shapes,
to words, or any other kind of object.
The object in a set is called its “elements” or “members” and they can be listed in curly brackets “{}” or specified by a common property or characteristics that all members of the set share.
For example: Let us consider
A={1,2,3,3} B={1,1,2,3}
here, we need to see whether we have any common number inside the curly braces. As we can see that 1,2,3 are common in both.
Sets can be manipulated using various
operations, such as union, intersection, and complement and they are a
fundamental concept in many branches of math, including set theory, algebra,
and geometry.
What is a Null set?
A null set is a set that has no elements
or members. It is an empty set that does not contain anything. It is like a box
with nothing inside.
It is denoted by the symbol “{}” or “Φ”. The null set is a subset of every set, including itself, and has a cardinality of Zero. The null set is also distinct from the set that contains a “null” or “undefined” value which may appear in another context.
For example:
1. A = { x | x is a month containing 32 days }
What is Singleton Set?
A singleton set is a set that contains
only one element. In other words, it is a set with a single member or item.
e.g., {3} is a singleton set that contains only the number 3. The term “Singleton”
comes from the fact that the set has only one element like a singleton comes
from the fact that the set has only one element.
What is a finite set?
A finite set is a collection or group
of items or elements that have a limited or specific number of items. In simple
terms, it is a set that has a definite, countable number of elements.
For example, the set {1,2,3,4,5} is a finite set because it has only 5 elements.
What is an infinite set?
An infinite set is a set that contains
an unlimited or infinite number of elements, meaning it has no endpoint and is continuous
endlessly.
It may consist of numbers, objects, or any other kind of item that can be grouped together in a set.
What is an Inequivalent set?
An inequivalent set is a group of
items or elements that cannot be compared or matched to another set because
they are fundamentally different or have unique properties.
They are equivalent or identical to any other set.
What is a Disjoint set?
A Disjoint set is a data structure used in computer science and mathematics to group together elements that do not share any common properties or features. It is like a set of unique and independent items that have no overlapping elements.
In simple terms, a disjoint set refers to a collection of distinct objects or groups that have no connection or relationship with each other.