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The use of S (as in VIIS to indicate 7 1 ⁄ 2) is attested in some ancient inscriptions [45] and also in the now rare apothecaries' system (usually in the form SS): [44] but while Roman numerals for whole numbers are essentially decimal, S does not correspond to 5 ⁄ 10, as one might expect, but 6 ⁄ 12.
The most recent recorded use of the long s typeset among English printed Bibles can be found in the Lunenburg, Massachusetts, 1826 printing by W. Greenough and Son. The same typeset was used for the 1826 printed later by W. Greenough and Son, and the statutes of the United Kingdom's colony Nova Scotia also used the long s as late as 1816. Some ...
3. Restriction of a function: if f is a function, and S is a subset of its domain, then | is the function with S as a domain that equals f on S. 4. Conditional probability: () denotes the probability of X given that the event E occurs. Also denoted (/); see "/". 5.
The number of binary strings of length n without an even number of consecutive 0 s or 1 s is 2F n. For example, out of the 16 binary strings of length 4, there are 2F 4 = 6 without an even number of consecutive 0 s or 1 s—they are 0001, 0111, 0101, 1000, 1010, 1110. There is an equivalent statement about subsets.
For s > 1, the series converges and ζ(s) > 1. Analytic continuation around the pole at s = 1 leads to a region of negative values, including ζ(−1) = − + 1 / 12 . In zeta function regularization, the series = is replaced by the series =.
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The three factor-pairs of 18 are (1, 18), (2, 9), and (3, 6). All three factor pairs will produce triples using the above equations. s = 1, t = 18 produces the triple [7, 24, 25] because x = 6 + 1 = 7, y = 6 + 18 = 24, z = 6 + 1 + 18 = 25. s = 2, t = 9 produces the triple [8, 15, 17] because x = 6 + 2 = 8, y = 6 + 9 = 15, z = 6 + 2 + 9 = 17.