@rmi But floating point is so useful! IEEE single-prevision needs only 32 bits of storage to exactly represent 0% of the real numbers. By using 64 bits, an IEEE double can exactly represent over four billion times as many, which is 0%!
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That reminds me of the reasoning that a stopped clock is nearly the best possible clock you can have: it's accurate twice a day, whereas most reasonable clocks aren't accurate even once a day (if the clock has a constant drift, however small, it will cross actual real time <=once after each time it's set).
