binäärijoukko

A binary set is a type of set used in computer science and mathematics. It is a set where each element can either be present or absent, similar to a binary digit (bit) which can be either 0 or 1. This concept is fundamental to understanding how data is represented and manipulated in digital systems.

Binary sets can be visualized as a collection of items, and for each item, a decision is made: is it in the set, or is it not? This binary nature makes them efficient for storage and processing. For example, a binary set could represent the set of prime numbers less than 10. In this case, the elements present would be 2, 3, 5, and 7, while 1, 4, 6, 8, and 9 would be absent.

In computing, binary sets are often implemented using bitmasks or arrays of booleans. A bitmask is a sequence of bits where each bit corresponds to an element. If the bit is set to 1, the element is in the set; if it's 0, the element is not. This allows for very compact representations of sets, especially when the universe of possible elements is large but the number of elements in the set is relatively small. Operations like union, intersection, and difference can be performed efficiently using bitwise logical operations. The concept is also closely related to characteristic functions, where a function maps elements of a universe to either 0 or 1, indicating membership in the set.