Finite and Infinite Sets
What is finite set in set theory?
When a set has finite number of elements, it is called a “Finite set”. It is a set of natural numbers i.e., positive integers and can be easily counted.
How do you determine cardinality of a finite set?
The number of elements in a finite set is known as the cardinality of that set. The cardinality of a finite set is expressed as n(A).
Are all subsets of an finite set a finite set?
Yes, every subset of a finite set is also finite. The subsets are determined by using the formula 2n .
How to determine if a set is finite or infinite?
A finite set has a starting and ending point, whereas an infinite set is endless from both the starting and ending. If a set consists countable number of elements then it is a Finite set and if the elements are uncountable then it is an Infinite set.
Is 0 (zero) infinite or finite set?
Zero is a finite number. We know that the cardinality of an empty set is zero and also zero represents the absence of null quantity of something, so, we can say that zero is a finite set.
Is there any symbol for finite set?
No, there is no particular symbol for representing a finite set. It is represented as a normal set with alphabets like A, M, S etc. For example: A = { 1,2,3,4} is a finite set.
Can you represent an infinite set Roster form?
Infinite sets can not be represented in roster form.
Practice Problems on Finite and Infinite Sets
Finite and infinite sets are two different parts of “Set theory” in mathematics. When a set has a finite number of elements, it is called a “Finite set” and when a set has an infinite number of elements, it is called an “Infinite set”. A finite set is countable, whereas an infinite set is uncountable. The elements in a finite set are natural numbers i.e., non-negative integers. We use dots in a set to represent an infinite set. In this articles we will discuss about the finite and infinite sets, their properties, solved problems and practice questions.
Finite Sets
A finite set has a finite or countable number of elements. It is a set of natural numbers i.e., positive integers and can be easily counted. It is expressed as P = {1, 2, 3, 4, . . ., n} for natural number n. For example, {5, 6, 7, 8} is a set of countable numbers. An empty set { } is also considered a finite set as it has zero elements i.e., P={ } or n(A) = 0.
Example of Fine Sets
- A set of days in a week: ( Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday )
- The set of natural numbers less than 10: {1, 2, 3, 4, 5, 6, 7, 8, 9}
- The set of vowels in the English alphabet: {a, e, i, o, u}
- The set of planets in the Solar System: {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}
Infinite Set
An infinite set, as the name suggests, has an infinite or uncountable number of elements. It is a set of all whole numbers including non-negative and negative integers. Infinite sets are also known as uncountable sets. We know that two infinite sets always form an infinite set. It is expressed as P = {0, 1, 2, 3, . . . }, a set of all the whole numbers.
Some examples of Infinite Sets are:
- Set of whole numbers
- Set of integers
- Line segments in a plane etc.