This case study examines the salient features of two individuals' reasoning when confronted with a task concerning the cardinality and associated cardinal number of equinumerous infinite sets. The APOS Theory was used as a framework to interpret their efforts to resolve the "infinite balls paradox" and one of its variants. These cases shed new light on the nuances involved in encapsulating, and de-encapsulating, a set theoretic concept of infinity. Implications for further research are discussed. [For the complete proceedings, see ED597799.]