Table of Contents
Understanding Integers
Integers are whole numbers, including 0, and positive integers, such as 1, 2, and 3. Negative integers are numbers that are less than 0, such as -1, -2, and -3. Integers can be represented on a number line, with 0 at the origin and positive integers to the right and negative integers to the left.
Rules of Integers
Integers are whole numbers and their opposites. The set of integers consists of the natural numbers, zero, and the negative integers. The natural numbers are the counting numbers: 1, 2, 3, 4, 5, 6, and so on. Zero is the number that represents nothing. The negative integers are the numbers that are less than zero: -1, -2, -3, and so on.
The Addition of Signed Integer Numbers
When two signed integers are added, the first step is to convert the numbers to unsigned integers. The sum of the unsigned integers is then computed, and the sign bit is set to the sign of the larger of the two unsigned integers.
Subtraction of Signed Integer Numbers
The subtraction of two signed integer numbers is just like the subtraction of two unsigned integer numbers, except that we need to take care when dealing with the sign bit.
If the numbers have the same sign, then we subtract the absolute values and keep the sign bit the same.
If the numbers have different signs, then we subtract the absolute values and change the sign bit of the result.
Multiplication and Division of Signed Integer Numbers
When multiplying or dividing signed integers, the signs of the numbers are taken into account.
For example, the signed integer 3 multiplied by the signed integer -5 equals -15.
Similarly, the signed integer 9 divided by the signed integer -3 equals 3.
Closure Property:
The closure property of a function states that the function is a function of its inputs and its outputs.
Commutative Property:
For all real numbers a and b, a + b = b + a.
For all real numbers a and b, a × b = b × a.
Distributive Property:
For any real numbers a, b, and c,
a(b+c) = ab+ac.
Additive Inverse Property:
If a and b are real numbers, then their additive inverse, denoted by -a and -b, respectively, is the number that, when added to a, results in 0, and, when added to b, results in -b. That is,
-a + a = 0 and -b + b = -b.
Multiplicative Inverse Property:
For every number a there is a number b such that a multiplied by b equals 1. This number is called the multiplicative inverse of a, and is denoted by b-1.
For example, the multiplicative inverse of 3 is 1/3, and the multiplicative inverse of -5 is 5/-5.
Identity Property of Integers:
The identity property of integers states that for every integer, there exists another integer that is its additive inverse. In other words, the sum of two integers is always equal to zero if and only if the two integers are opposites of each other.
Zero:
1. a quantity of no importance
2. a quantity that is negligible in comparison with another
3. a quantity that is not measurable
Positive Integers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100
Negative Integers:
A negative integer is a whole number that is less than zero. The symbol for a negative integer is “-“.
The following are all examples of negative integers:
-5
-4
-3
-2
-1
About Integers
Integers are whole numbers that can be positive, negative, or zero. Integers are the set of natural numbers and their opposites. The natural numbers are 1, 2, 3, 4, 5, and so on. The opposite of a number is the number that is the opposite of its sign. The opposite of a positive number is a negative number, and the opposite of a negative number is a positive number.
