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Nothing wrong with your maths. If the fastest you can travel is given by v, then the furthest galaxy you can eventually get to, is one that is presently at distance (just slightly less than) $(v/c)L$, where $c$ is the speed of light, and $L=c/H_0$ is the Hubble length (https://en.wikipedia.org/wiki/Hubble%27s_law#Hubble_length ~ 14.4 Billion light years). ...


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