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I consider it infinity because the limit as the denominator goes to 0 is infinity.

I see this with investments that have infinity ROI. If you get into an investment using only other people's money (OPM) and you make a profit then you have made x / 0. Saying I made an infinity return makes more logical sense than I made 0 return.

There's a saying about the difference between a mathematician and an engineer. If there is a $100 bill on a table and each step you take must be half the remaining distance or less the mathematician will never get there, but the engineer will get there no problem.

It's a non-sensical debate IMO but from the investing scenario that I described above, for all practical purposes, it makes more sense to consider it infinity.



> I consider it infinity because the limit as the denominator goes to 0 is infinity.

Note that this only works if the denominator approaches 0 from a positive side. Otherwise it's 0. This is the idea behind the extended real numbers.




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