Set and Closure Property

Set

A set is a collection of objects fulfilling the following two properties:

• Unordered: There’s no particular order of the objects in a set. It doesn’t matter if an object is the first or seventh.
• Distinct: All objects in the set are distinct.

Set notation

A set is mathematically represented by curly braces $\{\ \}$ and is typically denoted by a capital letter. In the case that mentioning all the elements isn’t feasible, we resort to the set builder notation. The set builder notation allows us to represent a set in a concise manner.

Examples of sets

Description	Mathematical Representation
Set of natural numbers not exceeding 10	$A = \{1,2,3,4,5,6,7,8,9,10\} \hspace{16mm}$ $A = \{x$ | $x \in N \wedge 1 \le x \le 10\}$
Set of $2 \times 2$ symmetric matrices	$M = \bigg\{ \begin{bmatrix} a&b\\b&c \end{bmatrix}$ | $a,b,c \in \R \bigg\}$
Set of linear equations in $n$ unknowns	$L = \{w_1x_1+\cdots + w_nx_n=b$

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