Here is my 5-minute take on why I think conceptualizing infinity as a part of mathematics is fundamentally wrong (I know it regards mathematics, but in this case it's a metaphysical approach and mathematics is not the main subject or goal, even if it's used to visualize it)

When you think of nothing you think of a imaginary concept of lack of existence which we can't experience or comprehend, yet we can use as a proxy for a state where part of our perception is unable to well... Perceive something, despite it's objective existence (example: air is imperceivable through any of the human senses, yet it does objectively exist). In other words 0 is a symbol that allows us to describe that state. You can't divide with it because the process of dividing is a process that is simply a perceivable representation of a concept of partitioning a defined amount of reality into a defined space. You can have a reality defined as non-existing. Then you divide 0 into a defined space and get 0 as there was no reality to begin with. But you can't have 0 space, as if you take any amount of reality and try to divide it into 0 (non-existent) space it breaks the fundamental rule of existence which is that anything that exists does so in a defined space. And if you try 0/0, so you try to divide non-existance into non-existing space you lose the point of doing such equation - you try to conceptualize something, that by definition has no concept. So it's pointless.

It's actually funny how mathematicians concluded that something as silly as conceptualizing this or any similar concepts as infinity is a valid option - it's not. Again, by basis and fundamental goal maths is supposed to describe and conceptualize in an organized matter reality in which we find ourselves. But if that's the case, the concept of infinity has no place in it. As (even though we can't properly comprehend it) according to what we can observe our reality is, in fact finite. Infinity comes from our inability to perceive beyond observable spectrum if reality, so if anything, ironically infinity is actually a purely human invention. And as such it is childish and immature to use it as a valid concept in something that is supposed to describe reality. Here is a proof that there is a finite amount of numbers: if you use the smallest possible scale (which is a single quark as far as I know right know) and use it to count numbers up, and fill the entire universe perfectly, so that there is no more space for another quark to fit in, you have reached the highest number that exists. That's because anything higher is simply not possible - you can't count, imagine, see or use such a number and it doesn't describe anything. In other words - it doesn't exist. Apply same logic to anything like 1.3333(3), √2 etc. And you get same conclusion - there is an end to it. When you fill the entire universe (or reality if universe is not the only thing in it) with that number that's when it ends. Someone might argue that universe or reality is infinite and you can never fill it up. Well according to the theory of cosmic inflation it in fact is not. And if anything there are more proofs that reality is finite than there are proofs that it's not. One very basic is simply lacks of common infinity outside of human perception. Everything that we describe as infinite is only so for us. On the other hand everything that exists despite us so far is finite.