I am trying to understand why there is this restriction that all but finitely many coordinates of an element in an infinite direct sum be 0. In my mind, direct sums are synonymous with direct products. What exactly is the difference?
Reason for all but finitely many coordinates for an element in an infinite direct sum be 0
0
$\begingroup$
abstract-algebra
-
1Direct sums are not synonymous with direct products, they are a different thing, and the difference is this restriction on the coordinates. – 2017-02-24
-
0So when do we use direct products and when do we use direct sums – 2017-02-24