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The graph of the absolute value function for real numbers Composition of absolute value with a cubic function in different orders. The real absolute value function is continuous everywhere. It is differentiable everywhere except for x = 0. It is monotonically decreasing on the interval (−∞, 0] and monotonically increasing on the interval [0 ...
The standard absolute value on the integers. The standard absolute value on the complex numbers.; The p-adic absolute value on the rational numbers.; If R is the field of rational functions over a field F and () is a fixed irreducible polynomial over F, then the following defines an absolute value on R: for () in R define | | to be , where () = () and ((), ()) = = ((), ()).
Logarithmic scale. A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences between the magnitudes of the numbers involved. Unlike a linear scale where each unit of distance corresponds to the same increment, on a logarithmic scale each ...
Illustration of ae plane, showing the absolute values (unsigned dotted line lengths) of the coordinates of the points (2, 3), (0, 0), (−3, 1), and (−1.5, −2.5). The first of these signed ordered pairs is the abscissa of the corresponding point, and the second value is its ordinate.
The absolute value function is continuous (i.e. it has no gaps). It is differentiable everywhere except at the point x = 0, where it makes a sharp turn as it crosses the y-axis. A cusp on the graph of a continuous function. At zero, the function is continuous but not differentiable.
The MAE is conceptually simpler and also easier to interpret than RMSE: it is simply the average absolute vertical or horizontal distance between each point in a scatter plot and the Y=X line. In other words, MAE is the average absolute difference between X and Y.
Sign function. In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether the sign of a given real number is positive or negative, or the given number is itself zero. In mathematical notation the sign function is often represented as or .
The distance along the line from the origin to the point z = x + yi is the modulus or absolute value of z. The angle θ is the argument of z. Argand diagram refers to a geometric plot of complex numbers as points z = x + iy using the horizontal x-axis as the real axis and the vertical y-axis as the imaginary axis. [3]