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RE: starship-design: Relativity

I kind of thought so...

Okay, first question:

If the limit of T (the time required to go from point A to point B) as v
approached c equals zero, why isn't the limit of ABbar (the length of the
worldline) as v approaches c equal to zero? I sort of understand how and why
it is actually shorter even though it isn't a straight line, but why doesn't
it go to zero as v approaches arbitrarily close to c? Or have I simply not
read far enough yet? Maybe I'm just totally confused?