un·ion / ˈyoōnyən/ • n. 1. the action or fact of joining or being joined, esp. in a political context: he was opposed to closer political or economic union with Europe | a currency union between the two countries. ∎  a state of harmony or agreement: they live in perfect union. ∎  a marriage: their union had not been blessed with children. 2. an organized association of workers formed to protect and further their rights and interests; a labor union: the National Farmers' Union. ∎  a club, society, or association formed by people with a common interest or purpose: members of the Students' Union. ∎ short for rugby union. ∎ Brit., hist. a number of parishes consolidated for the purposes of administering the Poor Laws. ∎  (also un·ion work·house or un·ion house) a workhouse set up by such a group of parishes. ∎  Brit. an association of independent churches for purposes of cooperation. 3. (also Un·ion) a political unit consisting of a number of states or provinces with the same central government, in particular: ∎  the U.S., esp. from its founding by the original thirteen states in 1787–90 to the secession of the Confederate states in 1860–61. ∎  (also the Fed·er·al Un·ion) the northern states of the U.S. that opposed the seceding Confederate states in the Civil War. 4. a building at a college or university used by students for recreation and other nonacademic activities. 5. Math. the set that comprises all the elements (and no others) contained in any of two or more given sets. ∎  the operation of forming such a set. 6. a pipe coupling. 7. a part of a flag with an emblem symbolizing national union, typically occupying the upper corner next to the staff.

union Act of Union in British history, either of the parliamentary acts by which the countries of the United Kingdom were brought together as a political whole. By the first Act of Union (1707) Scotland was joined with England to form Great Britain. The second Act of Union (1801) established the United Kingdom of Great Britain and Ireland. Wales had been incorporated with England in 1536.
Union flag the national flag of the United Kingdom, consisting of red and white crosses on a blue background and formed by combining the flags of St George, St Andrew, and St Patrick; the name Union Jack is now frequently used.
union is strength proverbial saying, mid 17th century; early classical versions include Homer's Iliad ‘even weak men have strength in unity’ and the Latin tag ‘force united is stronger’. (Unity is a popular alternative for union in this saying, especially when used as a trade-union slogan.)
Union Jack originally and properly a small Union flag flown as the jack of a ship (a small version of a national flag flown at the bow of a vessel in harbour to indicate its nationality); more generally, the Union flag in any size or adaptation, regarded as the national ensign.

See also State of the Union message.

union
1. of two sets. The set that results from combining the elements of two sets S and T, say, usually expressed as S ∪ T

∪ is regarded as an operation on sets, the union operation, which is commutative and associative. Symbolically S ∪ T = {x | x ∈ S or x ∈ T}

The union of S and the empty set is S. See also set algebra.

2. of two graphs, G₁ and G₂. The graph that includes all the vertices and edges of G₁ and G₂, i.e. that contains the union of the two sets of vertices and of the two sets of edges as its vertices and edges.

union act or fact of uniting or being united XV; body of units joined together XVII; textile fabric composed of two or more materials XIX. — (O)F. union or ecclL. ūniō, -ōn- the number one, unity, f. ūnus ONE; see -ION. U. flag, national flag introduced to symbolize the union of the crowns of England and Scotland XVII; u. jack, orig. small union flag flown as a jack (see JACK3) XVII.

Un·ion / ˈyoōnyən/ an industrial and residential township in northeastern New Jersey; pop. 50,024.