1. [n]  a set containing all and only the members of two or more given sets; "let C be the union of the sets A and B"
2. [n]  the shape or manner in which things come together and a connection is made
3. [v]  make contact or come together; "The two roads join here"
4. [v]  cause to become joined or linked
5. [v]  become part of; become a member of a group or organization; "He joined the Communist Party as a young man"
6. [v]  come into the company of; "She joined him for a drink"
7. [v]  be or become joined or united or linked; "The two streets connect to become a highway"; "Our paths joined"; "The travelers linked up again at the airport"

1. \Join\ (join), v. t. [imp. & p. p. {Joined}; p. pr. & vb.
   n. {Joining}.] [OE. joinen, joignen, F. joindre, fr. L.
   jungere to yoke, bind together, join; akin to jugum yoke. See
   {Yoke}, and cf. {Conjugal}, {Junction}, {Junta}.]
   1. To bring together, literally or figuratively; to place in
      contact; to connect; to couple; to unite; to combine; to
      associate; to add; to append.
            Woe unto them that join house to house. --Is. v. 8.
            Held up his left hand, which did flame and burn Like
            twenty torches joined.                --Shak.
            Thy tuneful voice with numbers join.  --Dryden.
   2. To associate one's self to; to be or become connected
      with; to league one's self with; to unite with; as, to
      join a party; to join the church.
            We jointly now to join no other head. --Dryden.
   3. To unite in marriage.
            He that joineth his virgin in matrimony. --Wyclif.
            What, therefore, God hath joined together, let not
            man put asunder.                      --Matt. xix.
                                                  6.
   4. To enjoin upon; to command. [Obs. & R.]
            They join them penance, as they call it. --Tyndale.
   5. To accept, or engage in, as a contest; as, to join
      encounter, battle, issue. --Milton.
   {To join battle}, {To join issue}. See under {Battle},
      {Issue}.
   Syn: To add; annex; unite; connect; combine; consociate;
        couple; link; append. See {Add}.
   

2. \Join\, v. i.
   To be contiguous, close, or in contact; to come together; to
   unite; to mingle; to form a union; as, the hones of the skull
   join; two rivers join.
         Whose house joined hard to the synagogue. --Acts xviii.
                                                  7.
         Should we again break thy commandments, and join in
         affinity with the people of these abominations? --Ezra
                                                  ix. 14.
         Nature and fortune joined to make thee great. --Shak.
   

3. \Join\, n. (Geom.)
   The line joining two points; the point common to two
   intersecting lines. --Henrici.
   

1. inner join (common) or outer join (less common).

2. least upper bound.