Difference Between Finite and Infinite Set

The basic difference between finite and infinite set is that finite set has a specific, countable number of elements, while an infinite set has an uncountable or endless number of elements.

Finite set

A finite set is a collection of distinct elements that has a specific, countable number of members, which can be zero or more. For example, the set of integers from 1 to 5 {1, 2, 3, 4, 5} is a finite set with five elements.

Infinite set

An infinite set is a set that has an uncountable or endless number of elements, such as the set of all natural numbers (1, 2, 3, …) or the set of all real numbers.

Finite set Vs infinite set

The key differences between finite and infinite sets are given below:

CharacteristicFinite SetInfinite Set
Number of ElementsLimited, countableUnlimited, often uncountable
Example{1, 2, 3, 4, 5}{1, 2, 3, …}
CountabilityFinite, specific countInfinite, no specific count
EndpointHas an endpointHas no endpoint
CardinalityHas a finite cardinalityHas an infinite cardinality
Subset of Itself?NoYes (infinite sets contain infinite subsets)
OperationsStandard set operations applyStandard set operations apply
EnumerationAll elements can be listedCannot list all elements

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