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I'd rather do my math with a machine even though it requires finite precision. How operations affect precision is well known and not difficult to keep track of.
by protonfish 8y ago
I'd rather do my math with a machine even though it requires finite precision. How operations affect precision is well known and not difficult to keep track of. You will only have "error accumulation," as you call it, if your desired precision is at the maximum that your computational machine can tolerate. So don't do that, and everything will work out fine.
- JadeNB 8y ago> You will only have "error accumulation," as you call it, if your desired precision is at the maximum that your computational machine can tolerate. This is not true. The tiniest of errors can accumulate arbitrarily—this is what it means to say the real numbers form an Archimedean number system; and so it is perfectly possible to get, say, the wrong integer part (a far coarser measure than the maximum precision that any modern machine can tolerate) by performing many successive operations on, say, a float.