Editing Support (mathematics) (section)

==Generalization==

If <math>M</math> is an arbitrary set containing zero, the concept of support is immediately generalizable to functions <math>f : X \to M.</math>  Support may also be defined for any [[algebraic structure]] with [[Identity element|identity]] (such as a [[Group (mathematics)|group]], [[monoid]], or [[composition algebra]]), in which the identity element assumes the role of zero. For instance, the family <math>\Z^{\N}</math> of functions from the [[natural numbers]] to the [[integers]] is the [[uncountable]] set of integer sequences.  The subfamily <math>\left\{ f \in \Z^{\N} : f \text{ has finite support } \right\}</math> is the countable set of all integer sequences that have only finitely many nonzero entries.

Functions of finite support are used in defining algebraic structures such as [[Group ring|group rings]] and [[Free abelian group|free abelian groups]].<ref>{{Cite book|title=Computational homology|last=Tomasz|first=Kaczynski|date=2004|publisher=Springer|others=Mischaikow, Konstantin Michael,, Mrozek, Marian|isbn=9780387215976|location=New York|pages=445|oclc=55897585}}</ref>