Infinity plus infinity equals infinity. Infinity times infinity equals infinity. Infinity divided by infinity equals, well, I'm not sure. It could be one or two or seventeen. Infinity minus infinity equals, I guess don't know that one either. It could be zero, but not always.
Zero divided by infinity is zero, but so is one divided by infinity or a billion divided by infinity. Infinity divided by zero is undefined. You can't do it. It violates the laws of mathematics. If you try it, the math police will lock you away for √-1 years.
There are different kinds of infinity. There's the common, everyday infinity that describes the set of counting numbers, as in 1,2,3...infinity. There's also an indescribably larger infinity that represents the number of points on a line. Oh, and there's the dreaded infinity plus shipping and handling.
How many different kinds of infinity are there? Well, it's infinite. What kind of infinity describes the infinite number of infinities. I don't know, neither does anyone.
We can describe infinity but our knowledge is finite, whereas infinity is, well, infinite. If you turn this into a fraction with the finite part on top you get zero. It appears that I know nothing about infinity. You should keep this in mind and probably ignore anything that I say on the subject (especially this last paragraph).