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A monotonically non-increasing function. Figure 3. A function that is not monotonic. In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. [1][2][3] This concept first arose in calculus, and was later generalized to the more abstract setting of order theory.
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average. Weight functions occur frequently in statistics and analysis ...
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906, [1] building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder in 1889. [2]
Dilution (equation) Dilution is the process of decreasing the concentration of a solute in a solution, usually simply by mixing with more solvent like adding more water to the solution. To dilute a solution means to add more solvent without the addition of more solute. The resulting solution is thoroughly mixed so as to ensure that all parts of ...
In the mathematical field of analysis, a well-known theorem describes the set of discontinuities of a monotone real-valued function of a real variable; all discontinuities of such a (monotone) function are necessarily jump discontinuities and there are at most countably many of them. Usually, this theorem appears in literature without a name.
Weighted arithmetic mean. The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also ...
5. Your exercise is too low-intensity. There’s nothing wrong with low-intensity movement, but if your workout routine is too gentle, it may not be helping you lose weight in the long run ...
Exponential growth is the inverse of logarithmic growth. Not all cases of growth at an always increasing rate are instances of exponential growth. For example the function grows at an ever increasing rate, but is very remote from growing exponentially. For example, when it grows at 3 times its size, but when it grows at 30% of its size.