Outline Of A Business Operation Video
Your Business' Operations Manual -- The Road from Growth Plan to Execution Outline Of A Business Operation.In mathematicsa set is a well-defined collection of distinct elements or members. Sets are ubiquitous in modern mathematics. The more specialized subject of set theory is part of the foundations of mathematicsfrom which nearly all of mathematics can be derived.
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The concept of a set emerged in mathematics at the end of the 19th century. Georg Cantor was one Outline Of A Business Operation the founders of set theory. A set is a gathering together into a whole of definite, distinct objects of our perception [Anschauung] or of our thought—which are called elements of the set.
A loose notion that allows any property without restriction to define a collection, leads to paradoxes. Axiomatic set theory takes the concept of a "set" as a primitive notionand the properties of sets are defined by axioms. Mathematical texts commonly use capital letters [14] [15] [16] in italic such as ABC to denote sets. A set can be defined either intensionallyextensionally Opeation or ostensively. The simplest intensional method of defining a set is by using a rule or semantic description: [19] [18].
Sets are not limited to collections of elements following simple rules, such as the sets in the examples above, however. Roster notation or enumeration notation is Outline Of A Business Operation method of defining a set by listing or enumerating the members of the set, [20] [21] [22] [23] [24] enclosing the list of members in curly brackets :.
This is an example of enumerative definition. For sets with many elements, especially Busniess following an implicit pattern, the list of members can be abbreviated using ellipsis " Article source sets have an endless list of elements. These are called infinite sets. For example, the Ot of integers, including Outline Of A Business Operation, negative and zero, is an infinite set. In roster notation, this set can be written with just one ellipsis:. Set-builder notation is another intensional method of describing a set, which is often found in mathematical texts. In this notation, the vertical bar " " means "such that", and the description can be interpreted as " F is the set of all numbers nsuch that n is an integer in the range from Outlinne to 19 inclusive".
Some authors use a colon ":" instead of the vertical bar. Halmos [37] draws the analogy that a box containing a hat is not the same as the hat. It can easily be proved that there is at most one set that contains only itself as a member. Different frameworks of set theory vary on whether a set is allowed to contain itself as a member, or not.
See Russell's paradox. B contains Aand is not equal to A. The empty set is a subset of every set, [41] and every set is a subset of itself: [42].
An Euler diagram is a graphical representation of a set as a closed loop, enclosing its elements, or the relationships between different sets, as closed loops. If two sets have no members in common, the loops do not overlap.
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This is distinct from a Venn diagramwhich shows all possible relations between two or more sets, with each loop overlapping the others. There are sets of such mathematical importance, to which mathematicians refer so frequently, that they have acquired special names and notational conventions to identify them. Many of these important sets are represented in mathematical texts using bold e.
P or blackboard bold e.
Each of the above sets of numbers has an infinite number of elements, and each can be considered to be a proper subset of the sets listed below it. The primes are used less frequently than the others outside of number theory and related fields.]
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