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Do' Then A +- X I? 0) x- (9 ... (9 A 1 :, d x'"<=>. (k -- €) 0 = (1 Xk" Xh" . . , xl" ' , ) for all vectors k such that I ::s:: k i ---: d i . Clearly v(A) = s, and ,u(A) = x Id. 11, the rows of the Cartesian product A are not distinct if anyone of the vectors Xi is not a set. If the vectors Xi are all of the same dimension, they may be considered as the columns of a matrix X, that is, Xi = Xi. The product Xl (>9 x 2 ':'J' . x' = Xl @ X 2 09 ... 09 x, may then be denoted by (il X, or alternatively by (2,IIY, where Y is the transpose of X.

5) accounts for the interest of the I-residue . , in a base ten or a base two nUlnber system) Inust, in practice, employ only a finite nunlber of digits. It is therefore often desirable to approxilnate a nunlber or by an integer. For this purpose two functions are defined: I. r, 2. r. Thus f3. 00J == -3. r f·rl· Moreover, n == bln -:- bJ + b 10 n for all integers n. Hence the integral quotient bJ is equivalent to the quantity q occurring in the defInition of the j-residue for the case j == O. 5 13 STRUCTURED OPERANDS Elementary operations Any operation defined on a single operand can be generalized to apply to each member of an array of related operands.

C. c. rOlllall. Standard nunleral Variable Alphabetic Nunlcric Italic. c. c. Italic nunleral Unnlarked Underscore Vector Lc. c. c. 8 Typographic conventions for classes of operands will be denoted by the )ame Greek letter. ju denotes the maxiIllum prefix (Sec. 10) of the logical vector u. g" E and I for the capitals epsilon and iota. Literals and variables The power of any nlathematical notation rests largely on the use of symbols to represent general quantities which, in given instances, are further specified by other quantities.

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