Way more than a billion. The sun will still be burning in a billion years. It'll have expanded to larger than the size of Earth's orbit, as it will be in its red giant phase, but it'll still be here.
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Ok that's interesting. and disappointing. I guess what I'm remembering was someone talking about the CMBR and how much it would suck for astrophysics if you couldn't see it anymore.
The strengh of a hero is defined by the weakness of his villains.