alt Hacker NewsDoes half of something have a limit? Not by its definition. Same thing with addition or multiplication. All of these only work with some concept of infinity.
We could redefine "half" to mean "half of whatever you're talking about until you get to some arbitrary limit", but doing that to all of arithmetic is going to wind up in a very odd place.
Half of something has a value, and that value is not infinity. You need to be more specific about how exactly do you get infinity from the fact that half of something has a value.