beagrie":3qytwpw5 said:

I had this thought after reading a sci-fi book. If we take space to have some kind of edge or boundry, can it still be considered infinate in a mathematical sense? What I mean by this is that when you say space is infinate, a lot people assume you mean it goes on forever. People also assume infinate is the largest number you can count to when in actual fact it's not a number at all and the very premise means you can't count to it.

Some of the terminology in sci-fi and the popular literature is unfortunate. In general relativity the universe is taken to be a 4-dimensional manifold with a Lorentzian metric, space-time. What are called "infinite" and "finite" are properly termed "open" and "closed" manifolds, respectively. In either case the manifold is without boundary. A closed manifold is a compact manifold without boundary.

If there were a boundary, there would in fact be something of a problem. The boundary of a 4-manifold with boundary is a 3-manifold with boundary. So a boundary for space-time would be a portion of the universe that would have only three dimensions, which does make good sense physically. What would those three dimensions be? Two of time and one of space? Three of space and no time ? A new set of physics would be required to describe what is going on in the boundary.

This does not make it impossible. But it is quite a bit more complicated that you might initially imagine.

Infinity is also a bit more complicated than you might imagine. There are mathematical theories of infinite numbers, called cardinal or ordinal numbers. There are actually different sizes of infinity -- in fact an infinite number of them. In any case you cannot count to infinity. The first infinite number is actually the cardinality of the natural numbers, which are called countable by definition, but you cannot count "to" that number. It is simply a reflection that the natural numbers are also called the "counting numbers". Since there is no largest natural number the counting process never stops.

beagrie":3qytwpw5 said:

The Universe has been discovered to be expanding at a rapid rate, and has been expanding atvarious rates since the big bang. As light from near the beginning of the universe is only just reaching us, it's not a great leap to accep that the universe is expanding faster than light can travel.

As nothing in this universe can move faster than light, is it fair to say that the universe is infinate to us? For no matter how far or fast we travel to the outer limits of the universe, we will never reach an edge or boundry (even I the edge of the universe is a solid wall of cheese) because it will always be moving away from us too fast to catch.

I'd like to hear any thoughts on this, even if it's to point me to an article where someone has already said what I've just said.

No it is not fair to say that the universe is "faster than us". It rather depends on what your particular question and perspective might be.

There is evidence that the universe is not only expanding but that the rate of expansion is accelerating. That is a relatively recent development, and it is not understood, It is not inconceivable that this is not so or that it may not be so in the future (I am not saying that such a conclusion is warranted at this time or that it is likely, just conceivable). Tenor twelve years ago it was believed that the rate of expansion was slowing due to gravity. In any case there are legitimate questions regarding the entire space-time manifold. Such questions include the topology of "space-like slices which is related to curvature. It is not the case that simply considering them to be "infinite", or more properly open, is at all helpful. In fact it makes moot some of the deeper questions of cosmology.

From a practical matter the universe, and for that matter the galaxy are so large that travel there is totally impractical given current technology or any technology that we can even imagine at this time. But those constraints have nothing to do with our ability to understand through the application of physics the universe in which we live. To apply physics an mathematics it is necessary to consider questions involving the entire space-time manifold, no matter how large it may be.