The purpose of this study was to examine the ways advanced mathematics students define "number" and the degree to which their definitions extend to different number domains. Of particular interest for this study are learners' fundamental conceptions of number and the implications for learners' interpretations of complex numbers (a + bi). Using the theoretical framework of number worlds and qualitative data from interviews, we examined students' foundational conceptions of number. We identified two distinct categories of participants' core definition of number, Physical and Symbolic. We compare these core definitions and the extent to which participants could stretch their definition of number to include other types of numbers. This study contributes an initial exploration into the number worlds of college students with substantial mathematical backgrounds.