Additive Identity for Integers
Additive identity is known as an identity as it does not alter the result even after the addition operation. The additive identity for integers is zero (0) as adding 0 to any number retains the same result. In this article, we will understand the property of additive identity for integers in both addition and subtraction of integers.
| 1. | What is the Additive Identity for Integers? |
| 2. | Additive Identity for Subtraction in Integers |
| 3. | FAQs on Additive Identity for Integers |
What is the Additive Identity for Integers?
The additive identity for integers is 0. The term identity is defined for any element that retains the same number to which it is added even after a change takes place. Its identity does not change and mathematically the value remains the same. Also, we know that 0 is the only number which when added to any quantity does not alter its value. Therefore, we can say that 0 acts as a mirror to a number, since adding 0 to an integer will give back the same result. This applies to all the integers. Let's understand this by taking an example - 5. When - 5 is added to 0, we get back the same number i.e., - 5 + 0 = - 5. Hence, we conclude that 0 is the additive identity for integers.
Given an integer a, its identity element will be 0 that is a + 0 = a and 0 + a = a. Therefore, a + 0 = 0 + a = a. For example, considering an integer 7, we see that 7 + 0 = 7. For a negative integer let's say - p, we will also have the identity element as 0 since - p + 0 = - p and 0 + (- p) = - p. Thus, - p + 0 = 0 + - p = - p. For example, considering a negative integer - 3, when 0 is added to - 3 i.e., - 3 + 0 = - 3, we get the sum as - 3.
Additive Identity for Subtraction in Integers
Just like the additive property of integers, we also have the subtractive property of integers also termed as subtractive property of zero. The arithmetic operation performed in this is the subtraction operation. This is based on the fact that whenever 0 is subtracted from a number, we get back the same result. So we see that subtraction of zero from any integer does not alter its value and the integer's identity is retained. Let's consider an integer a. We know that a - 0 = a. However, for an integer, a - 0 = a but 0 - a = - a. Thus, 0 does not satisfy the condition 0 - a, as we do not get back the same result. For example, for the number 9, we see that 9 - 0 = 9 but 0 - 9 = - 9. For a negative integer - p, we have - p - 0 = - p and 0 - (- p) = 0 + p = p. For example, for the number - 3, we get - 3 - 0 = - 3 but 0 - (-3) = 0 + 3 = 3. Therefore, 0 is not the identity element for the subtraction of integers.
Thus, for an integer y, the subtractive property states that y - 0 = y.
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FAQs on Additive Identity for Integers
What is the Additive Identity for Integers?
The additive identity for integers is zero (0) as adding 0 to any integer gives back the same number.
What is the Additive Identity for the Set of Integers?
The additive identity for the set of integers is equal to 0 which is also known as the identity element. This is because when 0 is added to an integer, the result does not change. For example, - 6 + 0 = - 6.
What is the Additive Identity for Integers and Whole Numbers?
The additive identity for integers and whole numbers is 0 as we know that when 0 is added with any number, it gives back the same result.
What is Additive Identity for Subtraction in Integers?
Subtracting 0 from any number equals the number itself. However, a - 0 = a but 0 - a = - a. Thus, 0 does not satisfy the condition 0 - a = - a, as we do not get back the same result. Therefore, 0 is not the identity element for the subtraction of integers.
What are the Multiplicative Identity and Additive Identity of Integers?
The additive identity for integers is 0 and the multiplicative identity for integers is 1. This is because when we add 0 to an integer we get back the same result and when we multiply any integer by 1, we get the same integer.