Kardinaliteedid

Kardinaliteedid refer to the concept of "cardinalities" in Estonian. In mathematics, cardinality is a measure of the number of elements in a set. For finite sets, this is simply the count of its members. For example, the set {apple, banana, cherry} has a cardinality of 3.

The concept becomes more nuanced when dealing with infinite sets. Different infinite sets can have different cardinalities. Georg Cantor introduced the idea of transfinite cardinal numbers to distinguish between these infinities. The cardinality of the set of natural numbers (1, 2, 3, ...) is denoted by aleph-null (ℵ₀). This is the smallest infinite cardinality.

Cantor proved that the set of real numbers has a larger cardinality than the set of natural numbers. This cardinality is often denoted by 'c' or 2^ℵ₀. The question of whether there exists a set with a cardinality strictly between ℵ₀ and 'c' is known as the continuum hypothesis. This hypothesis has been shown to be independent of the standard axioms of set theory.

In database theory and relational algebra, cardinality also refers to the number of rows in a table. It is distinct from the number of columns, which is referred to as arity. Understanding cardinality is fundamental to grasping set theory, different sizes of infinity, and is applied in various fields like computer science and logic.