Selective Sums and the Cantor Set

Tim Ferdinands, Alfred University

The sum of an absolutely convergent infinite series is a number.  A subsum of such a series also converges, but possibly to a different number.  A selective sum of an absolutely convergent series is defined as the subsum of that series.  The set of selective sums is the set of all subsums of the series. The set of selective sums of an absolutely convergent series can described topologically as one of three possibilities: (i) a finite union of intervals, (ii) a Cantor set, or (iii) a Cantorval.  In this talk we introduce the Cantor set and Cantorvals as well as discuss when the set of selective sums can be described in each of these ways.

Refreshments precede the talk at 3:30 p.m. in NH 282.