Matter. Its continually created, has no end. You cannot get rid of it. Take a piece of paper, that is matter. Now burn the paper, ashes remain. Matter. Place ashes in a cup of water. Matter. Place the water in a filter, what remains? Purified water and the ashes.
Matter is constantly created and can never be destroyed, the same goes for energy. We are full of energy. Energy is what power our hearts, our organs. Its what keeps us alive, when we die, that same energy is responsible for the decomposition of our bodies.
Before this solar system was created, back before the Universe became what it is today, whatever your belief in that is. There was matter, there was energy, because that energy and matter is what created the Universe. If you believe in the big bang or whatever other theory out there. It doesn't make much difference, its always there. That is infinity.
There are two ways to achieve infinity. Natural and man made. Man made is using technology like computers, and you're right, when the computer dies, or the man dies, the infinity ends. But that leaves nature. Mars is a dead planet, yet it still produces storms, rain still falls. So therefore, its not really "dead" its still alive, full of matter and energy. There are still rocks on the planet, that is matter. And they will remain there, forever.
Ok, I'll get it going a little. Was infinity just "made up" to account for the mathematical unknown? Error correction, perhaps?
Add one to one and keep adding one, there is no end...on and on we go so definitely in math infinity is real. They say that our planets circle the sun and all are moving into infinite space...on and on we go. I always felt just like the infinity symbol the figure eight would bring us back to the start. Of course if this was so the loop could almost be infinite in size. Is there a need for infinity...I don't know but the subject reminds me of this commercial.