Megszámolható

Megszámolható is a Hungarian term that translates to "countable" in English. In mathematics, specifically in set theory, a set is considered countable if its elements can be put into a one-to-one correspondence with the set of natural numbers (0, 1, 2, ...). This means that the elements of the set can be listed in an infinite sequence, even if that sequence never ends.

There are two types of countable sets: finite sets and countably infinite sets. A finite set is countable because its elements can be listed and the process of listing them terminates. A countably infinite set, on the other hand, can be put into a one-to-one correspondence with the set of all natural numbers. Examples of countably infinite sets include the set of integers (..., -2, -1, 0, 1, 2, ...) and the set of rational numbers.

The concept of countability is fundamental in understanding the sizes of infinite sets. While both countably infinite sets and the set of natural numbers are infinite, they have the "same size" in the sense that a bijection exists between them. Sets that are not countable are called uncountable. The most famous example of an uncountable set is the set of real numbers. The existence of uncountable sets demonstrates that there are different sizes of infinity.