Physics involves a LOT of mathematics. Mathematics involves a lot of arbitrary concepts. One of those concepts is the idea of infinity. This is the idea that something can go on and on forever, with no ending and it is the basis for a lot of modern theoretical science. It is speculated that the Universe itself may even be infinite in size and that time may also go on for ever. But is such a thing really possible? I would argue that it is not - although it can sometimes feel like it's real when you're at the back of the queue in the post office..
Let's take a standard 30cm ruler. It is divided into centimetres, and between those, millimetres. I assert that these divisions can only exist as they do BECAUSE there is no such thing as infinity. It's difficult to explain concepts such as infinity in words, mainly because it isn't something we usually experience in our day to day lives, but if the Universe were infinite (i.e it goes on forever and ever with no end) then I believe it is impossible to divide such a thing into smaller pieces. Each piece would itself be of infinite size. The very fact that we can have a mark on a ruler that says "this distance is 1mm" means that the ruler is not of infinite length. How can we have something of finite length contained within something of infinite length? In an infinite Universe nothing would have a position, a velocity or a momentum as these would all also be of an infinite value.
An argument may be made that the Universe itself is not infinite but only the space it can grow into is. Still, I think this boils down to the same issue: you cannot have something of finite size inside something of infinite size because something of infinite size cannot be broken down into smaller sections.
But what about numbers? Numbers can surely go on forever, right? There's no maximum number is there? Well, I would again argue that yes, there is a maximum number. Even though numbers can be seen as a sort of "virtual" object in that we can imagine them without having to write them down or have some physical object to display them, there STILL has to be some record of the number, somewhere... Even the human brain has limits. You could count as high as you could count but eventually (and I'm talking a REALLY long time) you would reach a number that contained too many digits for your brain to contain. There are only a certain number of neurones in the brain, and like a calculator, only enough "room" in there to hold a certain amount of information. Once this critical number was reached (again, I must stress that this would probably be a HUGE number) then the brain would simply not be able to envisage a number with any more digits in.
So what about a computer? It's the same thing essentially. You could probably keep increasing the count that the computer could reach by adding more and more memory to it but eventually (and now we're talking extreme hypothetical situations) you would end up filling the whole Universe with said memory and there would be no further the computer could go to. Unless, of course, the Universe was infinite - in which case the computer's memory chip would already be, by association, infinite as well. And, to sum up, this clearly isn't the case in our Universe.
There can be no such thing in real existence as infinity because anything within an infinite framework would itself be infinite; it would be unable to occupy a single position in space or time as there would be NO positions in space or time. Each point in space and time would also be of infinite size thus rendering the definition of a point useless.
Please feel free to comment on the above as this is only my opinion based on my own thoughts and I would like to hear other counter arguments.