Összeszámolhatók

Összeszámolhatók is a Hungarian term that translates to "countable" in English, particularly in the context of mathematics and set theory. It refers to sets whose elements can be put into a one-to-one correspondence with the natural numbers or a subset of the natural numbers.

There are two main types of countable sets. A set is countably infinite if its elements can be paired up with all the natural numbers (1, 2, 3, ...). Examples of countably infinite sets include the set of integers, the set of rational numbers, and the set of all finite strings over a given alphabet. Despite their seemingly vast nature, these sets have the same cardinality as the natural numbers, denoted by $\aleph_0$ (aleph-null).

A set is finite if its elements can be counted and the counting process terminates. This means there's a natural number $n$ such that the set has exactly $n$ elements. Finite sets can be considered a special case of countable sets, as their elements can be put into a one-to-one correspondence with the set $\{1, 2, ..., n\}$.

The concept of countability is fundamental in understanding the different sizes of infinity. Uncountable sets, such as the set of real numbers, contain more elements than the natural numbers, and thus cannot be put into a one-to-one correspondence with them. The study of countable and uncountable sets is a cornerstone of modern set theory and has significant implications in areas like computability theory and the foundations of mathematics.