Table of Contents

## Operations, Properties and Representation of Integers

Integers are whole numbers that can be represented by a sequence of digits. The number zero is the first integer, and every other number is a unique combination of some of the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Integers can be added, subtracted, multiplied, and divided. The operations of addition, subtraction, and multiplication are associative, meaning that the order of operations does not affect the result. For example, the sum of (2 + 3) and (4 + 5) is the same as the sum of (4 + 5) and (2 + 3).

The division of two integers can produce a quotient that is also an integer. For example, the quotient of 10 divided by 5 is 2, and the quotient of -5 divided by 2 is -2.5. When the dividend (the number being divided) is positive and the divisor (the number doing the dividing) is negative, the quotient is negative. For example, the quotient of 10 divided by -5 is -2. When the dividend is negative and the divisor is positive, the quotient is positive. For example, the quotient of -10 divided by 5 is 2.

Integers can be represented in base 10, which is the number system we use in everyday life. In base 10, the digits 0, 1, 2, 3,

## Symbol Representation

in C

C is a programming language that uses symbols to represent operations and values. In C, a symbol can be an identifier, a keyword, or a literal. An identifier is a name that refers to a variable, function, or other entity in a program. A keyword is a word that has a special meaning in C and is used to identify a specific type of entity. A literal is a value that is written directly into a program.

## Operation of Integers

Integers are a type of whole number that are used to represent positive and negative numbers. They are written using the symbol of a minus sign (-) to represent negative numbers and a plus sign (+) to represent positive numbers. The number zero is also considered an integer.

Integers can be used in mathematical operations, such as addition, subtraction, multiplication, and division. In order to perform these operations, the integers must be lined up so that the signs are aligned. For example, the following equation would result in a negative number:

-5 + 3

The following equation would result in a positive number:

5 + 3

## Algebraic Properties of Integers

Integers are algebraic objects. This means that they can be described by polynomials. For example, the integer 9 can be described by the polynomial x^3-x-1.

## Importance of Laws of Integers:

The laws of integers are important because they provide a basis for understanding the properties of addition, subtraction, multiplication, and division. These properties are essential for understanding mathematical operations and solving mathematical problems.