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Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was ...
- 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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Set Theory is a branch of mathematical logic where we learn sets and their properties. A set is a collection of objects or groups of objects. These objects are often called elements or members of a set. For example, a group of players in a cricket team is a set. Since the number of players in a cricket team could be only 11 at a time, thus we ...
- Set theory defines the collection of objects, where the order of objects does not matter. It relates with the collection of group of members or ele...
- The different types of sets are finite and infinite sets, subset, power set, empty set or null set, equal and equivalent sets, proper and improper...
- If we have two sets, P and Q, then, n(P U Q) = n(P) + (n(Q) – n (P ⋂ Q), where n denotes the number of elements. For three sets, P, Q and R, the...
- A singleton set has only one element. Example are {1}, {a}, {x:x is an integer that has only one factor}, etc.
- Sets can be represented in two different ways: Roster form and Set-builder form
Theorem 1.1.1 1.1. 1. Two sets A A and B B are equal if and only if A ⊂ B A ⊂ B and B ⊂ A B ⊂ A. If A ⊂ B A ⊂ B and A A does not equal B B, we say that A A is a proper subset of B B, and write A ⊊ B A ⊊ B. The set θ = {x: x ≠ x} θ = {x: x ≠ x} is called the empty set. This set clearly has no elements.
Sep 20, 2024 · set theory, branch of mathematics that deals with the properties of well-defined collections of objects, which may or may not be of a mathematical nature, such as numbers or functions. The theory is less valuable in direct application to ordinary experience than as a basis for precise and adaptable terminology for the definition of complex and sophisticated mathematical concepts.
Set theory. Set theory is a branch of mathematics that studies sets. Sets are a collection of (typically) well-defined objects. ... Definition/meaning Example ...
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Set theory is a branch of mathematics that studies sets, which are essentially collections of objects. For example \ (\ {1,2,3\}\) is a set, and so is \ (\ {\heartsuit, \spadesuit\}\). Set theory is important mainly because it serves as a foundation for the rest of mathematics--it provides the axioms from which the rest of mathematics is built up.
