It is infinite in the sense that there are parts of the universe in which lights haven’t been able to reach us.
Didn’t this start in GQ? (If so), why did it get moved to GD?
"Stephen Hawking has said that humanity is finally getting close to understanding the origin of the universe, speaking at a lecture in Hong Kong today.
The 64-year-old also said his unfulfilled ambitions, among many, were to find out what happens inside black holes, how the universe began and how the human race can survive in the next 100 years.
Above all, he joked, he wants to understand women."
Yes, but that’s not relevant here. In this context, “infinite” is a synonym for “unlimited”–no matter how much space you can see, there’s always more.
Is it then correct to postulate that if one were to travel at the speed of light for an infinite period of time you would just keep on going?
Forever, and quickly? To what ends would you arrive when you got there?
I still don’t get it.
You’re getting into the tricky business of mathematics involving infinity. I’m no expert, but I know enough to hurt your head worse (and yes, I think the vodka is a good idea).
Consider these two scenarios:
(a) I travel at the speed of light for an infinite period of time (as you suggested). How far have I gone? distance = speed x travel time, so I have traveled 186,000 miles per second x infinite seconds = an infinite distance
(b) I travel at a slow walking pace (2 miles an hour) for an infinite period of time. How far have I gone? 2 miles per hour x infinite hours = an infinite distance
A good example of how you can make infinite things bigger would be Hilbert’s Hotel
Whoa!
Gotta add an olive, now.
Appreciated the link. Thanks.
Yeah, but this is nothing difficult. Obviously there is an infinite number of positive integers. Obviously there is an infinite number of even positive integers. Obviously there are twice as many positive integers as even positive integers.
Similarly, not all integers are prime. But there are an infinite number of primes (proof, which is really easy, on request). Therefore the infinity of primes is smaller than the infinity of integers.
And so on. 
You’re joking, right?
In what way?
I am fairly certain that ultrafilter is referring to your statement that there are half as many even integers as there are total integers. Mathematically, it’s not true; there are exactly the same number of them. Of course, the “number” is infinity, which is why the concept is a little confusing.
The reason we can say for sure that there are the same number of integers and even integers is because we can come up with a function from the evens to the integers that is one-to-one and onto. Without going into the technical math, think of it like this: if I take all the even integers and divide them by two, the result is all integers. There is no integer that is not an even integer divided by two. So there must be the same number of elements (i.e. numbers) in each set if I can write out all the integers simply by starting with all the even integers and adding “over two.”
I hope that made some sense. I realize this has nothing to do with the actual topic, the infinite universe, but that’s how the cookie crumbles.
Indeed. And the more it crumbles, the nearer its surface area approaches infinity. 
Meaning, if you crumbled the cookie enough, the ultimate tiny crumbs would cover infinity?
O come on! Is that really explainable?
Or is my brain so small and limited, or just dumb?
No, the crumbs would have to be infinitely small, which can’t really happen in the physical world. Also, I’m not completely sure what you mean “the crumbs would cover infinity”, but it would be their surface area, not the space they take up that would be infinite.
Think about it like this: You have a cube. It has a cerain amount of surface area. Now, cut it in half. Now it has more surface area because you’ve created more surfaces. The more you do that, the more surface area you get, while retaining the same volume.
Additionally, a crumb is not a cube or even an approximation to one - it is a nasty in-and-outy fractal surface, and the closer you look at it, the rougher it gets. And the more you take that roughness into account, the bigger the surface area.
The tiny crumbs would do a poor job of covering infinity, but that fractal surface seems to be doing a better job the bigger and better your magnifying glass. 
So, are we saying that If the universe is constantly expanding, then it is correct to say the universe is not infinite at any specific point in time? Because in another minute or so the universe just got bigger, therefore at that specific point the universe was not infinite.
Just ask’n.
Nope. Suppose the universe is infinite in size, and then expands by a foot. How big is it ? Infinite ! By 100 light years ? Still infinite !
Confused? Who me?
If, say, " Suppose the universe is infinite in size" as you say. If then it got bigger was not it smaller by a foot or 100 light years before, as you say, it expanded, indicating it was not truly infinite at all five minutes earlier? You just thought it was?
God help us all, rather, kindly, won’t the muses be kinder to me?
Actually, I think I am getting closer.