What are the properties of $R$ used in the following? $0 + 0 = 0$

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Solution

We know that $0$ is the identity element under addition for the real numbers, since if $a$ is any real number then $a + 0 = 0 + a = a$

Now, since it is given that $0 + 0 = 0$ , therefore, $0$ is the identity element.

Hence, the identity element property of addition is used in $0 + 0 = 0$ .

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