Részhalmazoknak

Részhalmazoknak is a Hungarian term that translates to "subsets" in English when discussing mathematics. A subset is a fundamental concept in set theory. A set A is considered a subset of another set B if every element of A is also an element of B. This relationship is denoted by the symbol ⊂, so A ⊂ B means that A is a subset of B.

There are a couple of important special cases. The empty set, denoted by ∎ or {}, is considered a subset of every set. This is because the condition "every element of the empty set is also an element of B" is vacuously true, as there are no elements in the empty set to violate the condition. Also, every set is a subset of itself.

When A ⊂ B and A is not equal to B, then A is called a proper subset of B. This is denoted by the symbol ⊂. For example, if set A = {1, 2} and set B = {1, 2, 3}, then A is a proper subset of B because all elements of A are in B, and B contains an element (3) that is not in A.

The concept of subsets is crucial for understanding many areas of mathematics, including logic, combinatorics, and abstract algebra. It provides a way to describe relationships between collections of objects and forms the basis for more complex set operations like union, intersection, and difference.