infinite set
a set with an unlimited, or infinite, number of elements ( never ending)
An infinite set is a set that contains an uncountable number of elements or members. In contrast to a finite set, which has a specific number of elements, an infinite set has an endless number of members that can be added to or removed from it. Infinite sets can be either countable or uncountable.
A countable infinite set is an infinite set that can be put into a one-to-one correspondence with the set of natural numbers (positive integers) by assigning a unique natural number to each element of the set. Examples of countably infinite sets include the set of even numbers, the set of odd numbers, and the set of all integers.
An uncountable infinite set is an infinite set that cannot be put into a one-to-one correspondence with the set of natural numbers. Examples of uncountably infinite sets include the set of real numbers and the set of points on a line or in a plane.
The concept of infinite sets has many applications in mathematics, including calculus, topology, and number theory. It is also an important topic in the philosophy of mathematics and has been the subject of much debate among mathematicians and philosophers.
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