You can see back as far as the Big Bang, approximately 14 billion years ago, so all matter in the visible Universe is within 14 billion light years of the Earth. However, the space the Universe occupies is only really finite if it's positively curved. If it's flat or negatively curved, the space it occupies is infinite, and if its density is constant, it must contain an infinite amount of matter even though we only see part of it. The Big Bang is a singularity - a point with infinite density. It's hard to get your head around intuitively, but it all makes sense mathematically. (The maths is pretty hard, and rarely covered at undergraduate level.)

The simplest model in rough agreement with observations is called the Einstein-de Sitter Model, and it's flat with a zero cosmological constant. See http://www.britannica.com/science/cosmology-astronomy/Relati...

More general models are covered here: https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr...

Off the cuff thought: the overall universe is infinite and not expanding, and it's only the visible universe that's expanding into that infinite space.

Now try to wrap your mind around this: someone that's one light year to the left is going to see a slightly different visible universe, also expanding, into the same infinite space. But if we look in their direction, we see the edge of our visible universe expanding into the void, but from their point of view looking in the same direction our edge is one light year short of their edge. So what's our edge expanding into?

Math includes the idea of orders of infinity. There are infinite prime numbers, there are more positive integers, even more integers (positive and negative), even more rational numbers (A/B), and even more numbers (rational + irrational {e, Pi} etc)...

I don't know the answer to your question, but I can imagine how something can expand if it's infinite. Imagine an infinitelylong rubber band in front of you. Now imagine grabbing it with two hands and pulling them away from each other, causing the rubber band to stretch. If you take a sharpie, and paint dots on a spot representing planets or whatever else, they will pull away from eachother as you stretch the rubber band.

Take the set of positive integers (0, 1, 2…). Double them, so you have (0, 2, 4…). You had an infinite list of numbers, all "compact" (no room for more positive integers inbetween them), and with a simple mathematical transform, you've given yourself space for a second equally-sized infinity of integers to fit neatly inside of them.