When we talk about mathematics, we can say that all the numbers that don’t contain decimals are integers. On the left side of the number line, we write all the negative numbers, and on the right, we write all the positive numbers. Each integer has the property of being a whole number, which means that neither of them contains a decimal (fractional part). The numbers on the number line are all integers, whether they are negative or positive. There are also decimals between two whole numbers but these do not count as integers. Mathematics relies heavily on integers, and in this article, we will get an in-depth understanding of them.

What is Integer?

All positive and negative whole numbers can be referred to as integers. No fractional part should appear in the integers even if they are zero, positive or negative. In mathematics, most calculations are carried out using integers because they follow all arithmetic operations, such as addition, subtraction, multiplication, and division. As we discussed earlier, an integer contains no fractional part, so when it is divided by another number, there should not be any remainder and the result should be a whole number.

Subtracting a large negative number from a small positive number will produce a negative whole number, for example, 3 – 5 = -2, where -2 is a negative whole number and thus an integer. Integers include zero, natural numbers, can be positive or negative, and are referred to as counting numbers, whose symbol is Z. Listed below are the numbers that make up the set of integers as a whole:

• Positive integer: If an integer is greater than 0, it is considered positive. For example, 1, 2, 3, 4, 5 and so on are positive integers.

• Negative integer: If an integer is less than 0, it is considered negative. For example, -1, -2, -3, -4, -5 and so on are negative integers.

• Zero: Numerical value that is neither negative nor positive is considered zero and is whole numbers.

Hence, the set of integers can be written as:

Z = {… – 5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …}

Does Integer follow Arithmetic operations?

As with other types of numbers, integers are also subjected to arithmetic operations, let’s take a closer look:

• Addition of integers: Any integers can be added together regardless of whether they are positive or negative. The resulting integer can either be positive or negative depending on the two numbers. After adding two integers, the result is the sign of the larger number. This is an interesting aspect of integers. Whenever two integers are of the same sign, the result will also be of the same sign.

• Subtraction of integers: It is required that one of the integers be negative in order for the subtraction of integers to take place. Therefore, we can only get the difference between the two numbers. The sign of the result is dependent on the sign of the larger integer.

• Multiplication of integers: Multiplying integers is simply the addition of those many integers repeatedly, and the sign of the result derived from the multiplication of the sign can also be obtained. The following are some sign conventions when it comes to integer multiplication in mathematics:

• + x + ⇒ +
• + x – ⇒ –
• – x + ⇒ –
• – x – ⇒ +

• Division of integers: Previously, we discussed this aspect of integers previously in this article. Integers should be completely divisible to obtain an integer; if one number does not completely divide the other number, the result will be a decimal number, which is not considered an integer. The sign of the result can be obtained by dividing the signs of two results and we can write them as:

• + ÷ + = +
• + ÷ – = –
• – ÷ + = –
• – ÷ – = +

Does Integer Have Some Rules?

Since we have discussed so far, we can understand how important integers are in mathematics, hence there are some rules to keep in mind when doing those calculations, and those rules are as follows:

• Two positive integers added together will always result in a positive integer.
• Two negative integers added together will always result in a negative integer.
• The product of two positive integers will always result in a positive integer.
• The product of two negative integers will always result in a negative integer.
• The result of adding two positive integers with the same negative integer will be 0.

Conclusion

From what we have discussed in this article, we can conclude that integers play an extremely vital role in mathematics. This is especially when it comes to dealing with arithmetic calculations where the result depends on the sign and the value of the integers. This article covered topics such as the integers definition, their rules, and their properties, as well as how integers follow arithmetic calculations. Since the sign convention plays a significant role in arithmetic calculations when dealing with integers, they are very useful in various fields, such as physics, chemistry, etc. Therefore, it is crucial to have a deep understanding of what an integer is as well as how to use it. This would be helpful when one encounters them in higher education.