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Simple Sets and Indexing

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The document provides a detailed overview of AMPL's capabilities for linear programming, focusing on the fundamental concepts of sets and indexing. It explains various types of sets, including unordered and ordered sets, and discusses set operations such as union, intersection, and difference. The text emphasizes the importance of indexing expressions in modeling and illustrates how to define and manipulate sets effectively within AMPL. Additionally, it covers the use of ordered sets for better organization in models and introduces predefined intervals for common numerical ranges.

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What is the difference between indexed set and ordered set?

Indexed sets are build when you define a function between a totally-ordered set (as the domain) and an arbitrary set (in the codomain), then, the totally-ordered set you used becomes the index set, because you used it to index the arbitrary set.

What is the index of a set?

In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set A may be indexed or labeled by means of the elements of a set J, then J is an index set.

Can you index in sets?

Any set (finite or infinite) can be used as an indexing set. Often capital Greek letters are used to denote arbitrary indexing sets and small Greek letters to represent elements of these sets.

What is an example of index form?

Here is a number written in index form: 2 is the base number and 4 is the index or power. 24 is a short way of writing 2 2 2 2 . (read as squared) is a short way of writing a a .

What is an example of an index set?

An index set could be a set of any objects. For instance, the sets of numbers in the last example could be the favorite Lotto numbers of five different students. We could index these sets ing to the names of the students: AJohn={1,4,23},AMary={7,11,23},AJoe={3,6,9},APete={5,17,22},ALucy={3,6,23}.

What is index set with example?

A Simple Math Example Imagine you have a bag of marbles, each uniquely numbered from 1 to 10. By assigning an index to every marble, like a tiny ID card, we create an index set that helps us identify and work with each marble efficiently.

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