How is it possible that the universe is infinite if it has existed for a finite amount of time?

the universe is approximately (and it is funny to use that word with a measurement so large) 1 trillion light years in diameter, and increasing. so what it means when we say that it is infinite is that technically it is in that you would never be able to travel fast enough to get to the end of it. because like, since the big bang, the universe never stopped growing, and it's growing REALLY fast, at least at the speed of light, and since we cannot travel even that fast then it is technically "infinite." hope that added some clarity :)