In mathematics, the concept of an integer is very important. Integers are the numbers that include zero, all positive counting numbers, and all negatives of counting numbers. Therefore integers can be a positive number such as 1, 2, 3, 7, 58, 94 .. etc. or it can be negative numbers such as -1, -5, -26, -82.. etc. Zero is also an integer that is neither positive nor negative.
It becomes easier to visualize the positive and negative integers by putting them on a number line which is a straight line where numbers are placed at regular intervals sequentially. The central point is marked as zero (0) and integers are placed on both sides of zero. The positive integers are placed on the right of zero starting from left to right. The negative integers are put on the left side of zero starting from right to left. The value of numbers increases as we move rightwards from zero whereas the value of numbers decreases as we move towards the left starting from zero.
For example, the integer 6 is placed on the right side of integer 2 on the number line that means 6 > 2. Again, -5 is placed to the left of -3 starting from zero, therefore -5<-3. Any integer is greater than the integer placed on the left of it on the number line.
The integers are used for basic mathematical calculations like addition, subtraction, multiplication, and division.
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- When two integers are added, subtracted, multiplied, the result is always an integer.
- When one integer is divided by another integer, the result may not necessarily be an integer. When zero is added to an integer, the result is the same integer only. Here zero is called the additive identity of integers.
- The sum of an integer and its negative integer is zero. Here one integer is called the additive inverse of the other.
- Any integer when multiplied by 1, gives a product that is the same as the original integer.
- The addition and multiplication of integers follow the associative and commutative properties.
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