Set
A set is a collection of objects treated as a single object in its own right. Membership is the only thing that counts: order and repetition make no difference, so the set containing 1, 2 and 3 is the same set however it is written. Sets can contain other sets, and a set can be infinite. Almost every modern mathematical object, a number, a function, a shape, can be built out of sets, which is why set theory serves as a common foundation for the rest of the subject.
Why it matters
It is the smallest idea that everything else can be defined in terms of, which is why foundational disputes in mathematics are usually disputes about sets.
Also written: sets
Where it comes up
Sources
- Set (mathematics) Wikipedia
- Set theory Encyclopaedia BritannicaA short account of how sets came to be the standard foundation.
