Hilbert's paradox of the Grand Hotel - Wikipedia
read if you want but the point is that infinity is not a number. Infinity is a concept for never-ending. Infinity + 1 is still infinity because there is an infinite amount of numbers out there and adding 1 to infinity will still result in the concept of infinity as well.
We are unable to apply the rules for normal algebraic operations such as any number/it self=1 as infinity isn't a number, it's a concept.
Side note: Using infinity in operations is a pretty counter-intuitive thing, but it is commonly used for things such as limit, derivative, integral, infinite series, and other calculus and beyond subjects.
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Infinity is anonymous. There is no highest number, because we haven't found names for higher numbers, which, we never will. Even dividing infinity by 0 does not help.