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Why is an analog-to-digital converters not a counterexample? For that matter, why is a comparator (a one-bit ADC) not a counterexample? Or, for that matter, a

• kazinator 4y ago
  I think it's because these devices do not always make the correct decision between two values. Lamport's paper covers this in the interrupt example: a computer must decide whether an interrupt line is signaled or not in a finite amount of time (the next instruction). The interrupt is continuous: it passes through some halfway voltage level like 2.5 between 0 and 5, and so it can be called the wrong way. Basically the whole result is a restatement of real numbers not being computable. The discrete sample value you get from an ADC is not based on knowing the underlying real number absolutely, and then choosing the nearest value. It's a time limited process of discovering the value partially. Since the value is not partially known, it is not known whether the reported sample value is the closest one.