Difference Between Positive and Negative Numbers

# Difference Between Positive and Negative Numbers

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Vikram Singh
Assistant Manager - Content
Updated on Aug 29, 2023 13:54 IST

In mathematics, numbers are the basic building blocks of all mathematical concepts. In the previous articles, we have discussed rational, irrational, natural and whole numbers. All these numbers are either positive numbers or negative numbers. So, in this article, we will discuss all about positive and negative numbers.

Before starting the article, let’s discuss the number line.

Number Line: A number line is a horizontal line on which the numbers (especially integers) are placed at equal intervals. On the number line, zero is the middle point. All the positive numbers are arranged at the right of zero, and all the negative numbers are at the left.

Now, without further delay, let’s explore the difference between positive and negative numbers.

Table of Content

## Difference Between Positive and Negative Numbers

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## What are Positive Numbers?

Positive numbers are numbers greater than zero. It can be a natural number, whole number, positive integer, or fractions and are represented by plus (+) sign

Examples: 1, 22, 0.34, 3.14, 22/7

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### Properties of Positive Number

• Greater than zero: Positive numbers are number that is always greater than zero.

The sum of two positive numbers is always a positive number.

Example – 1: 2 + 2 = 4

• Closed under multiplication

The product of two positive numbers is always a positive number.

Example – 1: 2 * 2 = 4

Note: The product of two negative numbers is also a positive number.

Example: (-2) * (-2) = 4

• Additive Identity: When 0 is added to any number, it will return the same number.

Example: 2 + 0 = 0 + 2 = 2

• Commutative Property: Positive numbers are commutative in nature i.e., a + b = b + a

Example: 2 + 3 = 5 = 2 + 3

• Order Property: Every positive number can be ordered from least to greatest, i.e., if a and b are two number such that a is less than b then it is given by a < b.

Example: 2 < 3

• Existence of additive and multiplicative inverse

Every positive number has additive as well as multiplicative inverse.

• Multiplicative Inverse: 1/a is the multiplicative inverse of a.
Scalars and Vectors: Understanding the Key Differences
Physical quantity with magnitude and no direction is known as a scalar quantity and a physical quantity with magnitude and directions is known as a vector quantity. In this article,...read more
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Vectors are mathematical objects that contain both magnitude and direction, and they can be represented by the directed line segments (lines having directions) whose lengths are their magnitude. It is...read more
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## What are Negative Numbers?

Any number that is less than zero is called negative number. In simple terms all real number that are not positive numbers (except zero) are negative numbers.

Example: -0.24, -22/7, -3

### Properties of Negative Number

• Less than zero: Negative numbers are numbers that are always less than zero.
• Closed under addition: The sum of two negative numbers is always a negative number.

Example: -2 + (-2) = -4

• Commutative Property: Negative numbers are commutative in nature, i.e., if a and b are two negative numbers, then a + b = b + a

Example: -2 + (-3) = -5 = -3 + (-2)

• Existence of Additive inverse and multiplicative inverse: Every negative number has additive as well as multiplicative inverse.
• Multiplicative Inverse: 1/a is the multiplicative inverse of a.
Function in Mathematics: Definition, Types, and Examples
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Understanding Set Theory – What, Where, Why, and How do we use it in Data Science
Set in mathematics is a well-defined collection of objects that doesn’t vary from person to person. In this article, we will briefly discuss set theory, its representation, subset, cardinality, union...read more
Taylor Series Approximation: Definition, Formula, and Example
Let f(x) be a continuous and infinitely differentiable function (i.e., a function that can be differentiated infinite times), then the taylor series of f(x) is a series expansion of f(x) about a point x = a. In...read more

## Application of Positive and Negative Numbers

• Temperature: Positive numbers represent high temperature (high temperature represents high fever), whereas negative numbers represent negative temperature (when storing food in the freezer).
• Coordinates: Positive and negative numbers represent the co-ordinate in 2D and 3D.
• Physics: Positive and negative numbers represent force, velocity, and acceleration.
• Accounting: Positive and negative numbers represent credits and debits, respectively.
• Stock Market: Positive and negative numbers represent gain and loss in the stock market.
Types of Matrix
In Linear Algebra, Matrices are one of the most important topics of mathematics. The application of matrix is not just limited to mathematical solving problems; it has its applications across...read more
A matrix is a rectangular arrangement of numbers (real or complex) or symbols arranged in rows and columns. The number in the matrix are called the elements, and if the...read more
A skew-symmetric matrix is a square matrix whose transpose is equal to its negative. In other words, it is a matrix that satisfies the condition A^T = -A. This type...read more

## Conclusion

In this article, we have briefly discussed the positive and negative numbers, difference between them and their properties with the help of examples.

Hope you will like the article.

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## FAQs

What is a positive number?

Positive numbers are numbers greater than zero. It can be a natural number, whole number, positive integer, or fractions.

What is a negative number?

Any number that is less than zero is called negative number. In simple terms all real number that are not positive numbers (except zero) are negative numbers.

What is the difference between positive number and negative number?

Positive number is any number that is greater than zero, whereas any number less than zero is a negative number.