Infinity is like eternity, you never get there. If you are like me, your first foray into infinity came in math class in school. If you took the set of natural numbers, 1,2,3,4,5.... and on and on, you would see that there are an infinite many of them. My personal issue has to do with measurements. Particularly, The universe. Every time I read an article that describes something as infinitely big, infinitely small, infinitely dense, I feel a sharp pain in my side. Let me explain. The big bang was about 14 billion years ago according to best estimates. Then the universe should be at least 28 billion light years in diameter. Ah, but the universe is expanding at an accelerated rate you say. Alright then. The universe is larger still, but it isn't infinitely so because the universe is expanding every day. Is the universe more infinite today than it was yesterday? Infinity plus one? Max Tegmark has theorised that the next hubble volume similar to ours is 2**10**118 meters away. More zeroes than you could write in your lifetime, but still not infinitely far away. Lets go to the other end of the spectrum. Science tells us that inside a black hole is a singularity. A point with zero length. Science also tells us that the smallest possible unit of distance is the Planck length: 1.616199x10 ** -35 meters. A mind boggling small number to be sure, but not infinitely small. Also, the singularity has infinite density. Is this the same as having infinite mass?
Is the calculus we use to describe the universe not powerful enough? Is it that our understanding of the physics is not developed enough to explain what we see? Or is it the worst of my fears, when something is 50 or a 100 decimal places out, do we just call it a day with a sideways 8?
I don't know the answers to any of these questions. But I, like you since you are on this site, have a hunger for knowledge in science. Its just way too cool! I welcome discussion.