Assertion: abelian group's element | /r/HasProperty | requirement
Facets:
value: in the direct sum
type: OTHER
Source sentences:
text: An element in the direct product is an infinite sequence, such as (1,2,3,...) but in the direct sum, there would be a requirement that all but finitely many coordinates be zero, so the sequence (1,2,3,...) would be an element of the direct product but not of the direct sum, while (1,2,0,0,0,...) would be an element of both.