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Jan 23, 2010 at 14:54 comment added Hans-Peter Stricker If I think of $\mathbb{Z}$'s standard model (pairs of naturals in the von Neumann standard model) I would firstly think of the group $\mathbb{Z}/3\mathbb{Z}$ as a set consisting of three equivalence classes on $\mathbb{Z}$ and after that I would abstract from this model and think of the group abstractly (like you do in 1). It never would come into my mind, to think of this group as in 2.
Jan 22, 2010 at 15:45 history answered Reid Barton CC BY-SA 2.5