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A bijective (one-to-one and onto) correspondence between two structures that preserves the operations and relations of the structures, indicating they have the same form or structure. iteration The process of repeating a set of operations or a procedure multiple times, each time applying it to the result of the previous step. iteration theorem
In naive set theory, a set is described as a well-defined collection of objects. These objects are called the elements or members of the set. Objects can be anything: numbers, people, other sets, etc. For instance, 4 is a member of the set of all even integers. Clearly, the set of even numbers is infinitely large; there is no requirement that a ...
The power object of a set A is given by its power set, and the exponential object of the sets A and B is given by the set of all functions from A to B. Set is thus a topos (and in particular cartesian closed and exact in the sense of Barr). Set is not abelian, additive nor preadditive. Every non-empty set is an injective object in Set.
This is a category with a collection of objects A, B, C and collection of morphisms denoted f, g, g ∘ f, and the loops are the identity arrows. This category is typically denoted by a boldface 3 . In mathematics , a category (sometimes called an abstract category to distinguish it from a concrete category ) is a collection of "objects" that ...
Primarily denotes one hundred years, but occasionally used, especially in the context of competitive racing, to refer to something consisting of one hundred, as in a 100-mile race. Dozen: 12 A collection of twelve things or units from Old French dozaine "a dozen, a number of twelve" in various usages, from doze (12c.) [2] Baker's dozen: 13
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 ...
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions ...
The Gestalt law of proximity states that "objects or shapes that are close to one another appear to form groups". Even if the shapes, sizes, and objects are radically different, they will appear as a group if they are close. Refers to the way smaller elements are "assembled" in a composition.