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Message: [QUOTE="Mark Dickinson, post: 3534396"] Have you considered the fact that the real numbers of the form 1.xxxxx... are those in the range [1.0, 2.0], including *both* endpoints? That is, 2.0 = 1.999999... Similarly, the midpoint of this range can be written both in the form 1.500000... and 1.499999... This is relevant if you think of rounding as an operation on *decimal representations* of real numbers rather than as an operation on real numbers themselves. I'm not sure which point of view you're taking here. Either way, your arguments don't change the fact that the average rounding error is strictly positive for positive quantized results, under round-half-away-from-zero. Mark [/QUOTE]