Concept
Union (set theory)
Overview
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other.
A nullary union refers to a union of zero (
0
{\displaystyle 0}
) sets and it is by definition equal to the empty set.
For explanation of the symbols used in this article, refer to the table of mathematical symbols.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
But, while a series of mathematical points arranged in empty space expresses fairly well the process by which we form the idea of number, these mathematical points have a tendency to develop into lines in proportion as our attention is diverted from them, as if they were trying to reunite with one another. And when we look at number in its finished state, this union is an accomplished fact: the points have become…
Henri Bergson, Time and Free Will
States what Union is; names Union.
TABLE 4.28. Oxalis Regnelli (from Hildebrand). Column 1: Nature of the Union. Column 2: Number of Flowers fertilised. Column 3: Number of Capsules produced. Column 4: Average Number of Seeds per Capsule. Long-styled by pollen of longest stamens of short-styled. Legitimate union : 6 : 6 : 10.1.
Charles Darwin, The Different Forms of Flowers on Plants of the Same Species
Names Union several times.
Such a form of union is in principle a new organization, which is distinct, not only from the trade unions, but also from the revolutionary industrial unions in bourgeois society, just as the supremacy of the proletariat is distinct from the supremacy of the bourgeoisie. The productional union of the ruling working class no longer has the problems, the methods, the discipline, of the union for struggle of an…
Leon Trotsky, Dictatorship vs. Democracy
Names Union several times; states what Union is.
Philosophers who discussed Union (set theory)
Related ideas
- Finite set
- Georg Cantor
- Giuseppe Peano
- Parity (mathematics)
- Integer
- If and only if
- Zermelo–Fraenkel set theory
- Natural number
- Oxford English Dictionary
- Intersection (set theory)
- Power set
- Set (mathematics)
- Set theory
- Predicate (logic)
- Boolean algebra (structure)
- Axiom of extensionality
- Complement (set theory)
- De Morgan's laws
- Existential quantification
- Empty set
- Axiom of pairing
Place in the tradition
Part of Description logic.