From the first day that I entered college, I was wondering about the relationship between some basic mathematical abstract concepts and nature. I'm going to explain them here and you may find them a little bit opinion-based, but it's not. So please guide me in case you have good scientific-based answers/examples.
Infinity: Does infinity exist in reality? We all know it is an abstract concept but what I'm curious to know is if there are any physical phenomena out there that can show, stimulate or somehow help us understand the concept of infinity in reality/nature/the physical world.
Zero: What about Zeno's paradox? In nature (our physical world) there is a "smallest distance". It's about $1.6 \times 10^{-35}$ meters. Another example would be when someone says "there are three apples on the desk, if you take all of them there are $0$ apples on the desk". Obviously, it's an abstract concept, but what I would like to know is that if there is any observable physical event that can anyhow show us the concept of nothingness or absolute zero. E.g., we don't have absolute zero temperature in thermodynamics, absolute zero distance between 2 points in mechanics, or absolute zero gravity in a given space, etc.
Axiom of empty set: This axioms states:
"There is a set such that no element is a member of it."
One can imagine an empty set in nature as an absolutely empty box. But one can see it the other way around: the element "nothing" is there (quoting from Prof. Lawrence Krauss's book "nothing is something"). So, the same way one can say the element "nothing" is a member of a set. Obviously, it's an abstract concept and this may look like a play on words, but it's also an interesting paradox.
$\mathbb R$?! (the set of real numbers): There are millions of mathematical theorems which are based on $\mathbb R$! I wonder if there are any non-countable physical phenomena in the real world/nature?
Again, I know these mathematical concepts are just abstractions and help us to solve real-world problems! However, I'm more interested in the relation between these abstract concepts and our physical world/nature.