[Moon Double Comb]

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And, given that the Universe started as a singularity - i.e. spatially restricted to a single point - and a limited time has passed since then, and nothing can travel faster than the speed of light (relative to anything else) it could never have become (yet or in the future) spatially infinite.

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This is not true. It's possible for space itself to expand faster than c. Compare it if you will with the difference between phase and group velocity of a wave. The phase velocity can be greater than c. The group velocity not (which is basically the max velocity at which information can be transmitted).