Számolhatóak

Számolhatóak is a Hungarian term that translates to "countable" in English. It is primarily used in the context of mathematics, particularly in set theory. A set is considered számolható if its elements can be put into a one-to-one correspondence with the set of natural numbers {1, 2, 3, ...}. This means that even if the set is infinite, its elements can be listed in a sequence without missing any.

There are two main types of számolható sets: finite sets and countably infinite sets. A finite set has a limited number of elements, and is therefore trivially számolható. A countably infinite set, on the other hand, has an infinite number of elements, but these elements can still be enumerated. Examples of countably infinite sets include the set of all integers and the set of all rational numbers.

The concept of számolható is crucial for understanding the properties of different infinite sets. For instance, the set of real numbers is not számolható, meaning it cannot be put into a one-to-one correspondence with the natural numbers. This distinction is fundamental in areas like calculus and analysis. The study of számolható sets and their properties is a cornerstone of modern mathematics.