Abstract

An infinite series of real numbers is conditionally convergent if it converges, but the sums of the positive and of the negative terms are both divergent. How many infinite subsets of the naturals are necessary such that every conditionally convergent series has a subseries given by one of our infinite subsets that is divergent? The answer to this question is known as the subseries number ß, and was isolated as a cardinal characteristic of the continuum by Brendle, Brian and Hamkins.

In this talk we will consider several variants of the subseries number, where we restrict our attention to infinite subsets of the naturals that are also coinfinite. Due to this change, we may consider subseries produced by infinite coinfinite subsets of the naturals that remain convergent, producing various closely related cardinal characteristics of the continuum.