Set in mathematics and its types

Set is an important part of mathematics. Set in mathematics can be defined like this. "In real life well-defined collections, lists, or classes is called, Set."

Set in mathematics



Set in mathematics


Collections may be pens, animals, humans, rivers, countries anything like this. In a set, each of the collections is called an element or member of that set.

Name of a set, Elements of a set

A set is named with capital letters like A, B, C, D, etc. Set elements are small letters a, b, c, d, etc or numbers.

Let 23, 34, 24, 42 are elements of a set, and the name of that set is A. We have to write like this-

A= {23, 34, 24, 42}

Elements are written into the second bracket and separated with commas. This representation process is called tabular form.

Again,

Let in a set B elements are all the countries of South Asia. Here we can write,

B = {x: x is a country and situated in South Asia}

": " sign is called such that. This set representation style is called set building form. " | " sign is used also in some cases.

  • If a is an element of set A then a∈A is written. The sign ∈ is called belongs to. 
  • If a is an element of set A then we can say a belongs to A.
  • If b is not an element of set A then b∈A is written. It is called b is not belongs to A.

A= {23, 34, 24, 42} 

Here. 23∈A but 13∉A

Some types of sets

Empty set

 
If any set contains no element then the set is called an empty set. An empty Set in mathematics is defined by the ∅ sign.

Example:
∅ = { x : x² = 4 and x odd}
It is an empty set because by squaring any odd number we will not get x² = 4.

Remember: Empty set is not meaning {0}. This is meaning that this set has an element that is 0.

Disjoint set


If there is no common element between two sets then those two sets are called disjoint sets.

Example:

Let two sets are A= {1, 2, 3} and B = {4, 5, 6}. Between these two sets, there are no common elements. That is why these two sets can be called disjoint sets.

Subset


If all the elements of a set are also members of another set then the first set is called the subset of the second set.

Example:

Let two sets are A= {1, 2, 3, 4, 5} and B= {2, 4, 5}.

Here you can see that all the elements of set B are also the elements of set A. In this case set B is called the subset of set A. It is written as B⊂A.

If a set A is given then a lot of subsets can be made by taking one or more elements from that set.

Let a set is X = {1, 2, 3, 4, 5, 6, 7}

Some subsets from set X are {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 2, 3} etc.

With respect to the definition of subset set X is also a subset of set X. This type of subset is called an improper subset. Except for set X, all other subsets of set X are a proper subset.

Remember: An empty set is a subset of any set.

Finite set and Infinite set in mathematics


Finite set


If the limit of elements is defined for a set then the set is called a finite set.
Example: P = {5, 6, 8, 9}
{x : x is a vowel of letter}

Infinite set


Finite set: If the limit of elements is undefined for a set then the set is called a finite set.
Example: {2, 4, 6, 8, 10, ………….}
{x : x is real number}

So this was an overall discussion on Set in mathematics. Next, we have discussed some rules of the sets in mathematics.

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