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- Sets Definition. In mathematics, a set is defined as a well-defined collection of objects. Sets are named and represented using capital letters. In the set theory, the elements that a set comprises can be any kind of thing: people, letters of the alphabet, numbers, shapes, variables, etc.
- Representation of Sets in Set Theory. There are different set notations used for the representation of sets in set theory. They differ in the way in which the elements are listed.
- Sets Symbols. Set symbols are used to define the elements of a given set. The following table shows the set theory symbols and their meaning. Symbols. Meaning.
- Types of Sets. There are different types of sets in set theory. Some of these are singleton, finite, infinite, empty, etc. Singleton Sets. A set that has only one element is called a singleton set or also called a unit set.
Jul 19, 2024 · A set is a collection of well-defined objects that share some common property. It can be a group of any items, such as the names of the months in a year, the days in a week, or a list of variables or constants. Sets are named and represented in capital letters. Here are some examples of sets: A = {-5, -3, -1, 1, 3, 5} B = {2, 3, 5, 7, 11, 13, …}
- Set Theory Definition
- History of Set Theory
- Examples of Sets
- Important Terms Related to Set Theory
- Types of Sets
- Set Theory Symbols
- Set Theory Formulas
- De Morgan’s Laws
- Visual Representation of Sets Using Venn Diagram
- Conclusion – Set Theory
Sets are defined as ”a well-defined collection of objects”. Let’s say we have a set of Natural Numbersthen it will have all the natural numbers as its members and the collection of the numbers is well defined that they are natural numbers. Note: A set is always denoted by a capital letter. A set of Natural Numbers is given by: The above example is ...
The concept of Set Theory was propounded in the year 1874 by Georg Cantorin his paper name ‘On a Property of Collection of All Real Algebraic Numbers‘. His concept of Set Theory was later used by other mathematicians in giving various other theories such as Klein’s Encyclopedia and Russell Paradox. Sets Theory is a foundation for a better understan...
Some common examples of sets are mentioned below: 1. Set of Natural Numbers: N = {1, 2, 3, 4….} 2. Set of Even Numbers: E = {2, 4, 6, 8…} 3. Set of Prime Numbers: P = {2, 3, 5, 7,….} 4. Set of Integers: Z = {…, -4, -3, -2, -1, 0, 1, 2,….}
Some of the important terms related to sets are mentioned below. These terms will be used several times in this article, and knowing these terms will help you learn set theory.
There are different types of sets categorized on various parameters. Some types of sets are mentioned below:
Various symbols are used in Sets Theory. The notations and their explanation are tabulated below: Read More: Set Theory Symbols.
The set theory formulasare given for two sets – overlapping and disjoint sets. Let’s learn them separately
De Morgan’s Lawis applicable in relating the union and intersection of two sets via their complements. There are two laws under De Morgan’s Law. Let’s learn them briefly
Venn Diagramis a technique for representing the relation between two sets with the help of circles, generally intersecting. For Example: Two circles intersecting with each other with the common area merged into them represent the union of sets, and two intersecting circles with a common area highlighted represent the intersection of sets while two ...
We have covered all the concepts required to learn the set theory. We have covered the history, definition, examples, symbols, operations, and formulas of set theory. Set theory is an important topic and many questions come from set theory in many competitive Exams. Students should focus on set theory and practice with some questions provided in th...
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Oct 28, 2021 · If you remember your basic high school math, you'll probably recall mathematical set operations like union, intersection, difference and symmetric difference. Well, you can achieve the same thing with Python sets. 1. Set Union. The union of two sets is the set of all the elements of both the sets without duplicates.
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 sets it does not matter what order the elements are in. Example: {1,2,3,4} is the same set as {3,1,4,2} When we say order in sets we mean the size of the set. Another (better) name for this is cardinality. A finite set has finite order (or cardinality). An infinite set has infinite order (or cardinality).
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1. Write a set consisting of four small hand tools that might be in a toolbox and label it with a capital /**/T/**/. All the sets we have considered so far have been well-defined sets. A well-defined set clearly communicates whether an element is a member of the set or not.
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