We propose a foundational and theoretical amendment in the understanding of sender anonymity within the notion of anonymity sets with implications in schemes for anonymous connections. We introduce our extension, of the anonymity metric developed by Díaz et al., creating the new metric degree of undetectability. Using this metric, we construct and prove conditions establishing singleton set anonymity. We show yet another approach to singleton set anonymity through unlinkable pseudonyms. Thus, we demonstrate that anonymity is attainable even for singleton sets under right assumptions, countering the unquestioned core belief in this field, and opening possibilities for paradigm shifts in the design of schemes for anonymity connections that can remain robust under singleton participation, and in largly sparse networks.