>Ok, then there is nothing really in that definition that prohibits movement in one general direction.
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>Suppose, for the sake of argument, that all objects in the Universe are moving more or less in the same general direction. Suppose also that the objects closest to the 'goal' are moving fastest and those furthest from it moving slowest. That would mean that the distance (or relative separation) between us and those objects closest to the 'goal' would be expanding, and the distance between us and those objects furthest from the 'goal' would also be expanding - assuming, of course, that we are neither the closest nor the furthest object from that 'goal'.

One further clarification might be in order. If all objects - including ourselves - move in the same general direction, there is really no way to detect it. Only relative motion can be detected. Presumably, they saw some galaxy clusters moving faster than others, toward the unknown attractor. Those that are closer to it would feel a stronger attraction.

>>Whatever that means. One thing it does seem to mean is that far-away places in the Universe are receding from us faster than the speed of light (and that the limit of the visible Universe is only 13 billion years old, but 2-3 times that distance away, in light-years); although "locally", the speed of light is the upper speed limit. That is, the fabric of space itself is getting bigger, but objects can not move "within space" faster than the speed of light.
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>I'm not sure why it necessarily means they are moving faster than the [local] speed of light.

Precisely that part is assumed to be impossible - moving faster than the [local] speed of light.

> It assumes, does it not, that the universe is, in fact, infinite, and not finite but expanding?

Not necessarily. But the Universe is believed to be much larger than we can detect, even with instruments much more powerful than we currently have: there would be galaxies whose light, due to the fact that they are receding from us at a tremendous speed, can never reach us.