My understanding is that it would be true but for the fact that the longer those vectors get, the farther back in time they reach, and thus eventually reach into a time when stars did not exist and thus you hit the CMB instead. The stars you would have seen are in space that has moved away from us faster than c.
My understanding is that the universe is believed to be literally infinite in the three spatial dimensions that are familiar to us, and that its mass is also believed to be infinite. It really blows the mind.
Disclaimer: I'm a programmer not a physicist. :-)
EDIT: I did a little more reading on this. Answers are all over the place. But from what I can make out of the most recent sources, it seems that modern models treat the universe "as if" it were infinite although there is no way to know whether it is or not.
My understanding is that the universe is believed to be literally infinite in the three spatial dimensions that are familiar to us, and that its mass is also believed to be infinite. It really blows the mind.
Disclaimer: I'm a programmer not a physicist. :-)
EDIT: I did a little more reading on this. Answers are all over the place. But from what I can make out of the most recent sources, it seems that modern models treat the universe "as if" it were infinite although there is no way to know whether it is or not.