The universe is infinite!......Right?

We can't see the end of the universe right? Therefore it must go on forever, right? That is a very good assumption, however it has been disproven. This is what we call the "Olbers' Paradox". Okay, so the assumption is that the universe is infinite in space and time. Therefore every line of sight from earth should end at a star, and if the universe is infinitely old, than the light has had time to reach us. So without having to know a lot about astronomy you would know that neither is true. Also, it couldn't be dust. Why not? Because dust at some point would generate the same temperature as a star, in which it would re-radiate like a star. NOT POSSIBLE. Therefore we have concluded that the universe is finite in space and time. Either there are no stars in certain directions or the light hasn't had time to reach us.