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?
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closed as not a real question by Pete L. Clark, Mariano SuárezAlvarez♦, Theo JohnsonFreyd, S. Carnahan♦, Anton Geraschenko Jan 22 '10 at 18:36
It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.
Initial object in the category of commutative rings. 


To a number theorist, shouldn't $\mathbb Z$ be the world? 


Final object in the category of schemes. 


Just $\mathbb{Z}$ ? ;) 


An infinite discrete subset of $\mathbb R$. 

