Elements of a set

The objects which have one or more common properties to form a set is called elements of a set.

Every object has its own properties naturally. One or more properties of an object match with properties of another object in some cases. The collection of such objects form a set under these common properties. If the objects form a set under one or some common properties, the objects are called elements of the set.

Example

1.

Basic Example

An example set formed by objects

Apple, Banana, Orange, Watermelon and Strawberry are five objects. Every object is having its own properties, for example taste, color, benefits, weight, structure, and etc. but all these objects are having some common properties.

  1. Natural Gift of trees
  2. Healthy eatables

According to these properties, the objects Apple, Banana, Watermelon, Orange and Strawberry are collected as a set, known as fruits. Now, each object is called as an element.

It is a basic example for understanding the concept of elements. Now, let us understand it from mathematical point of view.

2.

Mathematical Examples

Geometric shapes as elements of a set

Triangle, square, rectangle, circle, ellipse and pentagon are six objects and they are often appeared in geometrical mathematics.

Every geometric object is having its own properties and structure. The geometric structure of each object is different to another object and the properties of each object may also different to properties of another object.

However, there is one common property which makes them as a set. All are closed geometric shapes and forms a set. Now, each object is known as an element.

numbers as elements of a set

The objects 1, 2, 3, 4, 5, 6, 7, 8 and 9 are some symbols, used as numbers to represent quantities mathematically. Each symbol is having its own properties.

  1. Each number is denoted by a symbol.
  2. Each number represents a quantity.

However, all these numbers are used to count objects, measure quantities and labeling on the things. The purpose of these numbers is same. Therefore, they are considered as a set and each object is called as an element.

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