The development of the mathematical concept of the infinite, through the reflections that arise from personal notions and perceptions and the analysis of some ideas of Galileo and Cantor, invites us to investigate the relationship between intuition and formalization for the understanding of the said concept. This paper aims to observe and describe the shift from intuition to formalization that Omar, a first-semester undergraduate student in applied mathematics, goes through when accounting for the number of objects between two equal mirrors, one in front of the other. The results indicate that the interaction between intuition and formalism is necessary for Omar to conceive of mathematical infinity. [For the complete proceedings, see ED658295.]