Nothing to it: precursors to a zero concept in preschoolers

Do young children understand the numerical value of empty sets prior to developing a concept of symbolic zero? Are empty sets represented as mental magnitudes? In order to investigate these questions, we tested 4-year old children and adults with a numerical ordering task in which the goal was to select two stimuli in ascending numerical order with occasional empty set stimuli. Both children and adults showed distance effects for empty sets. Children who were unable to order the symbol zero (e.g., 0<1), but who successfully ordered countable integers (e.g., 2<4) nevertheless showed distance effects with empty sets. These results suggest that empty sets are represented on the same numerical continuum as non-empty sets and that children represent empty sets numerically prior to understanding symbolic zero.