What does the word 'infinity' mean? The word infinity is derived from the Latin word "infinite", which means infinity and has no limit or end. As a result, infinity has become a popular and very ...
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.
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 ".
For infinity, that doesn't work; under any reasonable interpretation, $1+\infty=2+\infty$, but $1\ne2$. So while for some purposes it is useful to treat infinity as if it were a number, it is important to remember that it won't always act the way you've become accustomed to expect a number to act.
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).