Definition: Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics. The English word infinity derives from Latin infinitas, which can be translated as " unboundedness ", itself derived from the Greek word apeiros, meaning " endless ".
I know that $\infty/\infty$ is not generally defined. However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for
Similarly, the reals and the complex numbers each exclude infinity, so arithmetic isn't defined for it. You can extend those sets to include infinity - but then you have to extend the definition of the arithmetic operators, to cope with that extended set. And then, you need to start thinking about arithmetic differently.
so long as x is a finite number. Meaning, adding or subtracting a finite number to an infinity does not change its value, but I vaguely remember a YouTube video that talked about different kinds of infinities, such as ∞! but it was all well above my head. So the question is, does subtracting finite numbers from an infinity make it smaller?
If you subtract a finite number from an infinity, does the infinity ...
The mathematical reason: because there's no good way to decide what the product of the complex unit i and the symbol for infinity should mean (and further, because if you want to consider the product to be the limit of I * x as x tends to infinity, there's no preferred direction in which to let x move).