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A set is a collection of objects, yet the definition of a set, in mathematics, is one of the weirdest. It’s a mathematical concept that allows us to group similar objects. Is there a method in mathematics that can group analogous mathematical objects? A set is an example of such an object. Do you want to learn how? Let’s have a look!
A set is a well-defined collection of mathematical objects. These items might be anything, from people’s names to their ages/likes/dislikes; entities ranging from a simple number system to complex scientific data; and results of a single dice throw or coin toss to tests performed 100s or 1000s of times.
Example of a Set
A collection of well-defined items is referred to as a set. The term “well-defined” refers to the fact that it must be clear which items belong to the set and which do not. Because the flowers in the set are not well-defined, a bouquet of gorgeous flowers is not a set. The term “beautiful” is a personal one. A bouquet of exquisite flowers cannot be regarded as a set since what is attractive to one person may not be so to another. If we have a collection of red flowers, on the other hand, it will create a set because each red blossom will be included.
Conventions for Sets
The conventions that are utilised here are as follows:
- A capital letter is frequently used to indicate a set.
- Small letters are frequently used to symbolise the group’s elements (unless specified separately.)
- If ‘a’ is an element of ‘A,’ or if a “belongs to” A, it is written using the Greek symbol ϵ (Epsilon) between them in the traditional sense – a ϵ A
- If b is not a member of set A, then b “does not belong to” A, as indicated by the use of the symbol ϵ (Epsilon with a line through it) between them – a ϵ A.
- The phrases objects, elements, entities, and members are all interchangeable.
Representation of a Set
Sets can be represented in one of three ways. Let us go over each Representation of Set in-depth, using as many instances as possible.
1. Statement Form:
The well-defined descriptions of a set member are written in statement form and contained in curly brackets.
For instance, consider the group of odd numbers less than 5.
It can be represented as {odd numbers less than 5} in statement form.
2. Roster Form:
The Representation of Set within {} and separated by commas in the Roster Form. The elements’ order is not crucial in this form, but they must not be repeated. Tabular Form is another name for Roster Form.
Example:
- Natural Numbers Fewer Than 10 is a collection of natural numbers that are less than ten.
For example, 1, 2, 3, 4, 5, 6, 7, 8, 9 are all natural numbers.
Set N is {1, 2, 3, 4, 5, 6, 7, 8, 9} in Roster Form.
Set of Natural Numbers that divide 10
Y is equal to { 1, 2, 5, 10}
In the word elephant, W stands for the set of vowels.
W = {E, A}
Set Builder Form:
The set is well defined since a rule, a formula, or a statement is written within the pair of brackets. To become a member of the set in the set-builder form, all of the set’s elements must share a single property.
The element of the set is specified using the symbol ‘x’ or any other variable followed by a colon in this method of representation of a set. The sign ‘:’ or ‘|’ denotes such that, after which we write the property owned by the set’s elements and enclose the entire description in braces. The colon denotes ‘such that,’ whereas the brackets denote ‘set of all.’
The general form is, A = { x : property }.
Conclusion
With the help of its definition and examples, we have mastered the representation of Set. Then we learned about different ways to represent a set. We discovered that a set can be represented in three different ways. Then, with the help of examples, we learned each type in-depth, and finally, we solved some cases to reinforce our understanding of the concept.
