I've been reading a little bit about Cantor's work with transfinite numbers, and one point is confusing me. 

If my understanding is correct, the set of positive integers ω and the set of negative integers ω\* have the same cardinality (Aleph-0), but different order types. But it's simple for me to pull describe the first 3 ordinals in those sets because they have a single vector (incrementation or decrementation): [1,2,3,...] and [-1,-2,-3,...] This leads to confusion about how I describe the first 3 ordinals in the set of all integers because ℤ = [...,-3,-2,-1, 0, 1, 2, 3,...]

* What are the first three ordinal numbers in the set of all integers ℤ?