Why did mathematicians conceptualized infinity? Do they use it in any mathematical systems?
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Infinity is a consequence of math. For example, if we set up the rules of a series and say the series is 1+1+1+… Forever, infinity pops out as the solution.
Just because infinity can pop out from simple rules of math doesn’t mean it’s physically real. Early debates on infinity were often about what it could possibly mean in reality. Even now, when infinity pops out of solutions in physics equations, it’s usually a sign that the answer is wrong because the theory is incomplete in some way. However, not always. Black holes are a consequence of infinity: if you pack a finite mass into an arbitrarily small space, it becomes infinite density. Black holes are indeed real though. The breakdown is that we don’t really understand them so the infinite density thing is still potentially not accurate.
Anyway you can see infinity has practical application and appears. Another is calculus when we integrate indefinitely from 0 to infinity. There are also math systems about different scales of infinity in set theory. Countably infinite sets are things like counting numbers. They go on forever. But there are also uncountably infinite sets, like real numbers. Uncountably infinite sets can’t be counted (paired with the counting integers). And it keeps going, actually. There are ever higher levels of infinity bigger than the previous. I don’t know the application for these though so I’ll stop there.
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