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Closed vs Monoid - What's the difference?

closed | monoid |

As a adjective closed

is sealed, made inaccessible or impassable; not open.

As a verb closed

is (close).

As a noun monoid is

(mathematics) a set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.

closed

English

Adjective

(-)
  • Sealed, made inaccessible or impassable; not open
  • (of a store or business) Not operating or conducting trade
  • Not public.
    • closed source
    a closed committee
  • (topology, of a set) Having an open complement.
  • (mathematics, of a set) Such that its image under the specified operation is contained in it.
    • The set of integers is closed under addition: \forall x,y\in\mathbb{Z}\,x+y\in\mathbb{Z}.
  • (mathematics, logic, of a formula) Lacking a free variable.

    • Synonyms

    * shut

    See also

    * close

    Verb

    (head)
  • (close)

    • Anagrams

    * (l) ----

    monoid

    English

    Noun

    (en noun)
  • (mathematics) A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.

    • Hypernyms

    * semigroup

    Hyponyms

    * group

    See also

    * * category * groupoid * loop * magma * quasigroup * submonoid

    Anagrams

    * (l) ---- ==Serbo-Croatian==

    Noun