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For example, in the (enlargeable) figure on the right, the necessary conditions for a local maximum are similar to those of a function with only one variable. The first partial derivatives as to z (the variable to be maximized) are zero at the maximum (the glowing dot on top in the figure). The second partial derivatives are negative.
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
Variables are generally denoted by a single letter, most often from the Latin alphabet and less often from the Greek, which may be lowercase or capitalized. The letter may be followed by a subscript: a number (as in x 2), another variable (x i), a word or abbreviation of a word as a label (x total) or a mathematical expression (x 2i+1).
Attributes are closely related to variables. A variable is a logical set of attributes. [1] Variables can "vary" – for example, be high or low. [1] How high, or how low, is determined by the value of the attribute (and in fact, an attribute could be just the word "low" or "high"). [1] (For example see: Binary option)
[3]: 694 The work of Marius Nizolius (1498–1576) contains another early reference to the concept of multisets. [8] Athanasius Kircher found the number of multiset permutations when one element can be repeated. [9] Jean Prestet published a general rule for multiset permutations in 1675. [10] John Wallis explained this rule in more detail in ...
The word "cause" (or "causation") has multiple meanings in English.In philosophical terminology, "cause" can refer to necessary, sufficient, or contributing causes. In examining correlation, "cause" is most often used to mean "one contributing cause" (but not necessarily the only contributing cause).
In particular, one can no longer talk about the limit of a function at a point, but rather a limit or the set of limits at a point. A function is continuous at a limit point p of and in its domain if and only if f(p) is the (or, in the general case, a) limit of f(x) as x tends to p. There is another type of limit of a function, namely the ...
In work on Zermelo–Fraenkel set theory, the notion of class is informal, whereas other set theories, such as von Neumann–Bernays–Gödel set theory, axiomatize the notion of "proper class", e.g., as entities that are not members of another entity. A class that is not a set (informally in Zermelo–Fraenkel) is called a proper class, and a ...