To the algebraist, $\mathbb{Z}$ is just the free group with one generator. To the algebraic topologist, $\mathbb{Z}$ is just the fundamental group of the circle. To be glib, what do $\mathbb{Z}$ mean to you?
Post Closed as "not a real question" by Pete L. Clark, Mariano Suárez-Álvarez, Theo Johnson-Freyd, S. Carnahan♦, Anton Geraschenko