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This is taken care of by the "small enough" and that the "looks like" is informal. The small enough depends on your accuracy in measuring curvature. The "looks like" does not sound as formal as "locally flat" as both "local" and "flat" have precise mathematical definitions. I would also be fine with "looks flat in a small enough region" as "look" is informal.atyy said:But isn't this still wrong, since Minkowski space is flat, but spacetime in a small region is not necessarily flat?