Yep. Actually though, it would depend on your mindset if it matters or not... but the funny thing is, if you are very attached to the idea of thinking yourself as the original, and not a mere copy, you can bet your ass that the "copy" thinks the exact same thing. Knives out, I say whoever bleeds out last is the original.

Also, this whole continuity argument is a cop-out, IMO. I fail to subjectively (which is the only way that matters) experience continuity every night, and somehow, I live with that.