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1. That this is a paradigm example of reduction practically has the status of dogma in the philosophical literature on reduction. Unfortunately, this is entirely misguided. See Sklar's Physics and Chance for an extended discussion.
2. For a good introduction to the subtleties involved see Sklar, 1967, pp. 118--121.
3. It is best to think of this limit as (v/c)2 → 0 since (v/c)2 is a dimensionless quantity and so this limit will not depend on the units used to measure the velocity.