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In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144 ...
In the figure, the fraction 1/9000 is displayed in Excel. Although this number has a decimal representation that is an infinite string of ones, Excel displays only the leading 15 figures. In the second line, the number one is added to the fraction, and again Excel displays only 15 figures. In the third line, one is subtracted from the sum using ...
Excel's storage of numbers in binary format also affects its accuracy. [3] To illustrate, the lower figure tabulates the simple addition 1 + x − 1 for several values of x. All the values of x begin at the 15 th decimal, so Excel must take them into account. Before calculating the sum 1 + x, Excel first approximates x as a binary number
The Microsoft xls file format which is the default file format used in versions prior to 2007 had a capacity limit of 65,536 rows by 256 columns (2 16 and 2 8 respectively). [71] This presents a problem for people using larger datasets, and can result in data loss.
The best known example of an uncountable set is the set of all real numbers; Cantor's diagonal argument shows that this set is uncountable. The diagonalization proof technique can also be used to show that several other sets are uncountable, such as the set of all infinite sequences of natural numbers (see: (sequence A102288 in the OEIS)), and the set of all subsets of the set ...
A matrix is in reduced row echelon form (also called row canonical form) if it satisfies the following conditions: [5] It is in row echelon form. The leading entry in each nonzero row is 1 (called a leading one). Each column containing a leading 1 has zeros in all its other entries.
It features Excel Web Access, the client-side component which is used to render the worksheet on a browser, Excel Calculation Service which is the server side component which populates the worksheet with data and perform calculations, and Excel Web Services that extends Excel functionalities into individual web services.
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.