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Arbitrary rate means you can set it up so that you don't have to worry about it in practice.

If I served a site where people could check if their passwords leaked I would not worry if one in a million viewers got a false positive.



As I said, "not worrying about it in practice" isn't "the same problem." If that is hard to wrap your mind around, you can suppose a fine of $1 billion for every wrong answer.


Engineering is all about tradeoffs. In real life things never work 100% reliably. Not being able to do tradeoffs disqualifies person as an engineer.

plonk


Algorithms are about correctness. Being incorrect disqualifies an algorithm as a solution to a problem.




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