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This proof is known as Dirichlet’s approximation theorem. At first blush, it only guarantees a single 2-good approximation for every real. Worse yet, the solution guaranteed by the proof might not comply with the rules of our game, because nothing stops it from producing exact approximations (ε = 0). So, what did we achieve?
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В удаленном от Украины почти в 2 тысячи километров регионе России ввели дистант из-за БПЛА08:47
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I think it's somewhat clear that with this narrower meaning, we can group a system in modules, but still have a full view of it that allows us to study its reliability and correctness at the whole system level, because there's no “abstracting” going on.