Signpost sequence
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In mathematics and apportionment theory, a signpost sequence is a sequence of real numbers, called signposts, used in defining generalized rounding rules. A signpost sequence defines a set of signposts that mark the boundaries between neighboring whole numbers: a real number less than the signpost is rounded down, while numbers greater than the signpost are rounded up. Signposts allow for a more general concept of rounding than the usual one. For example, the signposts of the rounding rule "always round down" (truncation) are given by the signpost sequence s_0 = 1, s_1 = 2, s_2 = 3 \dots
In mathematics and apportionment theory, a signpost sequence is a sequence of real numbers, called signposts, used in defining generalized rounding rules. A signpost sequence defines a set of signposts that mark the boundaries between neighboring whole numbers: a real number less than the signpost is rounded down, while numbers greater than the signpost are rounded up. Signposts allow for a more general concept of rounding than the usual one. For example, the signposts of the rounding rule "always round down" (truncation) are given by the signpost sequence s_0 = 1, s_1 = 2, s_2 = 3 \dots \operatorname{round}(x) = \begin{cases} \lfloor x \rfloor & x s(\lfloor x \rfloor) \end{cases} Where exact equality can be handled with any tie-breaking rule, most often by rounding to the nearest even.
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