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:
| Characteristic | Finite Set | Infinite Set |
| Number of Elements | Limited, countable | Unlimited, often uncountable |
| Example | {1, 2, 3, 4, 5} | {1, 2, 3, …} |
| Countability | Finite, specific count | Infinite, no specific count |
| Endpoint | Has an endpoint | Has no endpoint |
| Cardinality | Has a finite cardinality | Has an infinite cardinality |
| Subset of Itself? | No | Yes (infinite sets contain infinite subsets) |
| Operations | Standard set operations apply | Standard set operations apply |
| Enumeration | All elements can be listed | Cannot list all elements |