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In the top figure the fraction 1/9000 in Excel is displayed. 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 ...
The key feature of spreadsheets is the ability for a formula to refer to the contents of other cells, which may, in turn, be the result of a formula. To make such a formula, one replaces a number with a cell reference. For instance, the formula =5*C10 would produce the result of multiplying the value in cell C10 by the number 5.
Note that self-decomposable aggregation functions can be combined (formally, taking the product) by applying them separately, so for instance one can compute both the SUM and COUNT at the same time, by tracking two numbers. More generally, one can define a decomposable aggregation function f as one that can be expressed as the composition of a ...
In basic operation, Numbers can be used just like Excel; data can be typed anywhere, and formulas can be created by referring to the data by its cell. However, if the user types a header into the table, something one normally does as a matter of course, Numbers uses this to automatically construct a named range for the cells on that row or column.
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. Because the sum in the second line has only eleven 1's after the decimal, the difference when 1 is subtracted from this displayed value is three 0's followed by a string of eleven 1's.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
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However, there are infinitely many rational triangular numbers, rational generalized pentagonal numbers and rational tetrahedral numbers which are also magic constants of rational order. The term magic constant or magic sum is similarly applied to other "magic" figures such as magic stars and magic cubes. Number shapes on a triangular grid ...