# Linked Questions

3answers
404 views

### Can absolute convergent series be expressed as sum of two series?

Let $C\subset \omega \bigwedge A\bigcap B = \emptyset \bigwedge A\bigcup B = C$. Let $\{x_i\}$ be a sequence of nonnegative reals. Suppose $C$ is infinite and $\sum_{i\in C} x_i$ converges. (Since ...
1answer
300 views

### Convergence of Series of a Net's terms

I'm working through Dr. Pete Clark's convergence notes here: http://math.uga.edu/~pete/convergence.pdf and I've been thinking about Exercise 3.2.2 (a) and I am completely stumped. The exercise says ...
0answers
294 views

### Are uncountable “Schauder-like” bases studied/used?

We could define the following notion of basis in a way analogous to unconditional Schauder basis: If $X$ is a topological vector space over $\mathbb R$ and $B=\{b_i; i\in I\}$ be a subset of $X$. ...
0answers
264 views

### Would an integral defined using partitions of an interval into infinitely many intervals make sense?

In the definition of Riemann integral or Darboux-integral we first study partitions (or tagged partition) of the given interval determined by finitely many points. To each partition and a function $f$ ...
1answer
142 views

0answers
45 views

### Uncountably infinite series [duplicate]

I was fascinated when I heard that the most intuitive laws of arithmetic are no longer necessarily valid when it comes to the sum of an infinite sequence, which be denoted by S = \sum_{n=0,1,2,...}...

15 30 50 per page