In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a setA may be indexed or labeled by means of a set J, then J is an index set. The indexing consists of a surjective function from J onto A and the indexed collection is typically called an (indexed) family, often written as (Aj)j∈J.
Examples
An enumeration of a set S gives an index set , where f: J → S is the particular enumeration of S.
The set of all the functions is an uncountable set indexed by .
Other uses
In computational complexity theory and cryptography, an index set is a set for which there exists an algorithm I that can sample the set efficiently; i.e., on input 1n, I can efficiently select a poly(n)-bit long element from the set.
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by HowardHanson (1960) in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as AllenForte (1973), drawing on the work in twelve-tone theory of Milton Babbitt. The concepts of set theory are very general and can be applied to tonal and atonal styles in any equally tempered tuning system, and to some extent more generally than that.
One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, inversion, and complementation. The methods of musical set theory are sometimes applied to the analysis of rhythm as well.
Mathematical set theory versus musical set theory
Although musical set theory is often thought to involve the application of mathematical set theory to music, there are numerous differences between the methods and terminology of the two. For example, musicians use the terms transposition and inversion where mathematicians would use translation and reflection.
Furthermore, where musical set theory refers to ordered sets, mathematics would normally refer to tuples or sequences (though mathematics does speak of ordered sets, and although these can be seen to include the musical kind in some sense, they are far more involved).
A set (pitch set, pitch-class set, set class, set form, set genus, pitch collection) in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example.
A set by itself does not necessarily possess any additional structure, such as an ordering. Nevertheless, it is often musically important to consider sets that are equipped with an order relation (called segments); in such contexts, bare sets are often referred to as "unordered", for the sake of emphasis.
Two-element sets are called dyads, three-element sets trichords (occasionally "triads", though this is easily confused with the traditional meaning of the word triad). Sets of higher cardinalities are called tetrachords (or tetrads), pentachords (or pentads), hexachords (or hexads), heptachords (heptads or, sometimes, mixing Latin and Greek roots, "septachords"—e.g.,), octachords (octads), nonachords (nonads), decachords (decads), undecachords, and, finally, the dodecachord.
Set construction is the process by which a construction manager undertakes to build full scale scenery suitable for viewing by camera, as specified by a production designer or art director working in collaboration with the director of a production to create a set for a theatrical, film or television production. The set designer produces a scale model, scale drawings, paint elevations (a scale painting supplied to the scenic painter of each element that requires painting), and research about props, textures, and so on. Scale drawings typically include a groundplan, elevation, and section of the complete set, as well as more detailed drawings of individual scenic elements which, in theatrical productions, may be static, flown, or built onto scenery wagons. Models and paint elevations are frequently hand-produced, though in recent years, many Production Designers and most commercial theatres have begun producing scale drawings with the aid of computer drafting programs such as AutoCAD or Vectorworks.
In computing, associative containers refer to a group of class templates in the standard library of the C++ programming language that implement ordered associative arrays. Being templates, they can be used to store arbitrary elements, such as integers or custom classes. The following containers are defined in the current revision of the C++ standard: set, map, multiset, multimap. Each of these containers differ only on constraints placed on their elements.
Key uniqueness: in map and set each key must be unique. multimap and multiset do not have this restriction.
Element composition: in map and multimap each element is composed from a key and a mapped value. In set and multiset each element is key; there are no mapped values.
Family is an American television drama series that aired on the ABC television network from 1976 to 1980. Creative control of the show was split among executive producers Leonard Goldberg, Aaron Spelling and Mike Nichols. A total of 86 episodes were produced. It is not related to the ABC sitcom A New Kind of Family that aired concurrently with Family during its final season.
Premise
The show featured Sada Thompson and James Broderick as Kate and Doug Lawrence, a happily married middle-class couple living at 1230 Holland Street in Pasadena, California. Doug was an independent lawyer and Kate was a housewife (she would eventually go back to school). They had three children: Nancy (portrayed by Elayne Heilveil in the original mini-series and later by Meredith Baxter Birney), Willie (Gary Frank), and Letitia, nicknamed "Buddy" (Kristy McNichol). (There was another son, Timothy, who had died five years prior to the series' beginning.) The show raised the profile of all of its featured actors during its run and, in particular, catapulted McNichol to stardom.
A family of musical instruments is a grouping of several different but related sizes or types of instruments. Some schemes of musical instrument classification, such as the Hornbostel-Sachs system, are based on a hierarchy of instrument families and families of families.
Family relationships are not always clear-cut. For example, some authorities regard families as encompassing only instruments of different pitch range that have similar construction and tone quality. They therefore, for example, do not regard the cor anglais as a member of the oboe family, because its narrow bore and piriform bell give it a distinctly different tone quality from the oboe.
We look at the notion of indexed sets as well as their intersections and unions.
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1.4: Indexed Collections of Sets
published: 26 Jan 2013
Lesson 4: Intro to Indexed sets and Example 1
published: 06 Sep 2020
[Discrete Mathematics] Indexed Sets and Well Ordering Principle
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Index set with Examples| Partition of a Set| Set Theory 05| CBSE | JEE|set theory
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Set theory -05|partition of a set with Examples| CBSE | JEE
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Set Index App ကို ဒေါ်လာရှိနေမှသုံးလို့ရနေတာမဟုတ်ပါဘူးနော်တစ်ပြားမှမကုန်ရအောင်သုံးနည်း။
Get Set Code - Deep Dive into Forge App Development
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Index set -Definition and example by doleshwar kesharwani sir
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Today we discuss indexed sets and the well ordering principle.
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8 Things You Should NEVER Do With Your Valve Index...
Today I'm going over some less commonly talked about VR Tips regarding preserving your Valve Index. Unfor...
8 Things You Should NEVER Do With Your Valve Index...
Today I'm going over some less commonly talked about VR Tips regarding preserving your Valve Index. Unfortunately the Index is riddled with hardware problems so keeping your hardware in good condition is key. This should be especially useful for anyone jumping from Oculus to Index.
Like and Subscribe if you enjoy my content.
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8 Things You Should NEVER Do With Your Valve Index...
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Like and Subscribe if you enjoy my content.
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I'm like the monkey you send into space for tests. I just come back with the results and give them to you for FREE.
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#jayanta_sir, #partition_of_a_set, #Index_set, #math_tutorial
Titel of vedio:
Set theory -05|partition of a set with Examples| CBSE | JEE
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Titel of vedio:
Set theory -05|partition of a set with Examples| CBSE | JEE
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Titel of vedio:
Set theory -05|partition of a set with Examples| CBSE | JEE
Hi Guys,
I am Jayanta Pramanik, and welcome to my Gaming channel - Math Tutorial (Hindi)
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About This Channel:
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#Episode2 -
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Discrete Mathematics 2: https://www.youtube.com/playlist?list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2
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Discrete Mathematics and Its Applications (Rosen): https://amzn.to/3lUgrMI
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Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
8 Things You Should NEVER Do With Your Valve Index...
Today I'm going over some less commonly talked about VR Tips regarding preserving your Valve Index. Unfortunately the Index is riddled with hardware problems so keeping your hardware in good condition is key. This should be especially useful for anyone jumping from Oculus to Index.
Like and Subscribe if you enjoy my content.
----------------------------------------------------------------------
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Outro Song: https://www.youtube.com/watch?v=czUaNaDjK9k&list=PL0SUPYdGkDOuwhmI6X3vFceUWeemSwbjo&index=8
My channel is about VR Content (obviously lol) I've covered many topics on this channel in the past such as PC Building, PC Gaming Knowledge, Gaming News. That can be CPM rates, Industry knowledge, Business knowledge, how to edit, how to build a gaming PC, budget or not. But VR is cooler so I'm probably gonna keep doing that.
I'm like the monkey you send into space for tests. I just come back with the results and give them to you for FREE.
Some Tags: #GetHip #ValveIndex Oculus, Quest 2 , Review, Valve Index
#jayanta_sir, #partition_of_a_set, #Index_set, #math_tutorial
Titel of vedio:
Set theory -05|partition of a set with Examples| CBSE | JEE
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In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a setA may be indexed or labeled by means of a set J, then J is an index set. The indexing consists of a surjective function from J onto A and the indexed collection is typically called an (indexed) family, often written as (Aj)j∈J.
Examples
An enumeration of a set S gives an index set , where f: J → S is the particular enumeration of S.
The set of all the functions is an uncountable set indexed by .
Other uses
In computational complexity theory and cryptography, an index set is a set for which there exists an algorithm I that can sample the set efficiently; i.e., on input 1n, I can efficiently select a poly(n)-bit long element from the set.