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Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
Versions of Excel up to 7.0 had a limitation in the size of their data sets of 16K (2 14 = 16 384) rows. Versions 8.0 through 11.0 could handle 64K (2 16 = 65 536) rows and 256 columns (2 8 as label 'IV'). Version 12.0 onwards, including the current Version 16.x, can handle over 1M (2 20 = 1 048 576) rows, and 16 384 (2 14, labeled as column ...
More generally, there are d! possible orders for a given array, one for each permutation of dimensions (with row-major and column-order just 2 special cases), although the lists of stride values are not necessarily permutations of each other, e.g., in the 2-by-3 example above, the strides are (3,1) for row-major and (1,2) for column-major.
Under zero-based numbering, the initial element is sometimes termed the zeroth element, [1] rather than the first element; zeroth is a coined ordinal number corresponding to the number zero. In some cases, an object or value that does not (originally) belong to a given sequence, but which could be naturally placed before its initial element ...
Number blocks, which can be used for counting. Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. . The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the ...
For p an odd prime, count all digits greater than (p + 1) / 2; also count digits equal to (p + 1) / 2 unless final; and count digits equal to (p − 1) / 2 if not final and the next digit is counted. [2] The only known odd Catalan numbers that do not have last digit 5 are C 0 = 1, C 1 = 1, C 7 = 429, C 31, C 127 and C 255.
In fact, two of the three methods that all COM objects must provide (in the IUnknown interface) increment or decrement the reference count. Much of the Windows Shell and many Windows applications (including MS Internet Explorer , MS Office , and countless third-party products) are built on COM, demonstrating the viability of reference counting ...
The definition extends naturally to more than two random variables. We say that n {\displaystyle n} random variables X 1 , … , X n {\displaystyle X_{1},\ldots ,X_{n}} are i.i.d. if they are independent (see further Independence (probability theory) § More than two random variables ) and identically distributed, i.e. if and only if