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The last two examples illustrate what happens if x is a rather small number. In the second from last example, x = 1.110111⋯111 × 2 −50 ; 15 bits altogether. The binary is replaced very crudely by a single power of 2 (in this example, 2 −49) and its decimal equivalent is used.
Although such departures are usually beyond the 15th decimal, exceptions do occur, especially for very large or very small numbers. Serious errors can occur if decisions are made based upon automated comparisons of numbers (for example, using the Excel If function), as equality of two numbers can be unpredictable. [citation needed]
The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4.The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1.
atan2(y, x) returns the angle θ between the positive x-axis and the ray from the origin to the point (x, y), confined to (−π, π].Graph of (,) over /. In computing and mathematics, the function atan2 is the 2-argument arctangent.
A few steps of the bisection method applied over the starting range [a 1;b 1].The bigger red dot is the root of the function. In mathematics, the bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs.
Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive ...
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Numbers works in a fashion somewhat different from traditional spreadsheets like Microsoft Excel or Lotus 1-2-3. In the traditional model, the table is the first-class citizen of the system, acting as both the primary interface for work and as the container for other types of media like charts or digital images .
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