The Universe and questions regarding it.

Whao... Who said anything is expanding at the speed of light...The only thing that moves at the speed of light is light.

Strictly speaking, the first of your questions belong to physical cosmology, not philosophy. This does not mean they are not good questions - they are very good questions. But they are also very big questions. I suggest looking up some titles by Brian Greene and Paul Davies, both of whom write excellent books on these topics for a non-specialist audience.

As regards the nature of ideas, that it is also another very large question. I have only bits and pieces of an answer. One is to try and get a handle on what Plato meant by 'Ideas' and 'Forms'. This is not necessarily an easy thing to do, but then, these are big questions. But think about this. Mathematical ideas in particular are not the product of individual minds, in that they are the same for all minds. Yet they don't 'exist' anywhere in the physical universe. Those who believe that number is real in this sense, are known as mathematical realists. It is still quite a popular outlook, especially amongst mathematicians (as you can imagine).

Now the difference between mathematical ideas and your imaginary purple man is that, as I noted, maths is the same for everyone. This does not mean that everyone can understand all the ideas in it, mind you. But also it is not just the product of the individual mind. It is something basic to the fabric of reality.

maths is the same for everyone. [. . . . ] it is not just the product of the individual mind. It is something basic to the fabric of reality.

animals do not possess the same ability to learn the basic concepts of arithmetic

It seems to me that mathematical structures and techniques are products of individual minds.

Then why are they the same for everyone?

why do different people have different abilities to grasp them?

When I do understand it, this is something I now see. I could not see it before, now I can see it. There is no way it is a creation of my mind.

I regard number as a non-empirical attribute of reality.

how do you explain mathematical pathologies, for example, the Bannach-Tarski paradox?

4 does not equal 3 for anyone, regardless of their opinion. Same with euclid's proofs.

Curious, then, that maths can be used to lob shells onto targets, or rockets to the moon, with pinpoint precision, isn't it?

So in the case of maths, the way it is defined is not arbitrary, it is?

Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. In this point of view, there is really one sort of mathematics that can be discovered: Triangles, for example, are real entities, not the creations of the human mind.

Many working mathematicians have been mathematical realists; they see themselves as discoverers of naturally occurring objects. Examples include Paul Erdős and continuum hypothesis

What guarantee is there that some other life form will know what Pi means?

And maths is arbitrary, if maths were some species of feature of reality, how could Lagrange and Hamilton be equivalent, but mathematically distinct, descriptions?

How can maths be 'arbitrary'?

I have had several questions that I always asked myself from the first time I opened a physics/philosophy textbook when I was 12. Can somebody please help me in clarifying my confusion?

If the universe is constantly expanding at the speed of light, then wouldn't that mean everything within the universe is also expanding too, disregarding noticeably or not?

If the universe is infinitely large, then why is it expanding if it is already infinite?

Which brings me to my next question: can infinity and infinite energy/mass/matter etc. exist in this world? To have a value we need a comparison of at least two quantities or qualities. These comparisons serve as standards. Can infinity really exist if there will always be something greater than infinity, or if infinity is existence in a sense, will infinity always be infinite?

Also, if matter cannot be created or destroyed, and if the BBT were to serve as a validated explanation for this principle, how can our universe "force" itself into nothingness with its rate of expansion? Think of our universe as an egg. Think of a basket with a hole in it as the nothingness of space. If eggs are constantly dropped and never filling the basket, will the universe infinitely exist?

Something that is destroyed is created, something that is created is destroyed, right? If I break a stick in half, and I keep on breaking it until there is nothing left of that stick, would that mean that stick has been destroyed? Or, on a smaller scale, do the atoms that gave that stick its composition still continue to exist, albeit just floating around somewhere in the ethos?

If the universe is constantly expanding at the speed of light, then wouldn't that mean everything within the universe is also expanding too, disregarding noticeably or not?

If the universe is infinitely large, then why is it expanding if it is already infinite?

Which brings me to my next question: can infinity and infinite energy/mass/matter etc. exist in this world? To have a value we need a comparison of at least two quantities or qualities. These comparisons serve as standards. Can infinity really exist if there will always be something greater than infinity, or if infinity is existence in a sense, will infinity always be infinite?

Also, if matter cannot be created or destroyed, and if the BBT were to serve as a validated explanation for this principle, how can our universe "force" itself into nothingness with its rate of expansion? Think of our universe as an egg. Think of a basket with a hole in it as the nothingness of space. If eggs are constantly dropped and never filling the basket, will the universe infinitely exist?

Something that is destroyed is created, something that is created is destroyed, right? If I break a stick in half, and I keep on breaking it until there is nothing left of that stick, would that mean that stick has been destroyed? Or, on a smaller scale, do the atoms that gave that stick its composition still continue to exist, albeit just floating around somewhere in the ethos?

Also, my last question, which should be the most interesting of all. Are ideas infinite, or at least until humans die? Also, were all ideas that once "existed" always conceived into existence, or do ideas contain existence if we give it existence? It's pretty obvious that ideas are only ideas if they do not exist in a purely physical state of speaking. Soooo...If I think of purple humans that measure 30 feet tall, how can I be for sure that this idea has not been harbored into existence by someone else's mind? Existence and realism puzzles me, I don't get it.