Category:Generalized Sum Restricted to Non-zero Summands

This category contains pages concerning Generalized Sum Restricted to Non-zero Summands:

Let $G$ be a commutative topological semigroup with identity $0_G$.

Let $\family{g_i}_{i \in I}$ be an indexed family of elements of $G$.

Let $J = \set{i \in I : g_i \ne 0_G}$

Let $h \in G$.

Then:

the generalized sum $\ds \sum_{i \mathop \in I} g_i$ converges to $h$

if and only if:

the generalized sum $\ds \sum_{j \mathop \in J} g_j$ converges to $h$