Existence of addition identity: The integer 0 is called the additive identity.

Existence of additive identity

Why is 0 called additive identity?

Existence of additive inverse

Property 4 (Existence of addition identity): There is integer 0such that for any integer am we have a+0=a=0+a The integer 0 is called the additive identity.

Which integer is its own additive identity?

What is the additive identity of -6?

Existence of multiplicative identity

What is the value of additive identity of integers divided by multiplicative identity of integers?

When we add zero to any whole number we get the same whole number Zero is called the additive identity for whole numbers .Is it an additive identity again for integers also Observe the following and fill in the blanks (i) (-8)+0=-8 (ii) 0+(-8)=-8 (iii) (-23) +0= (iv) 0+(-37)=-37 (v) 0+(-59)=... (vi) 0+...=-43 (vii) -61 +....=-43 (vii) -61 +...=-61 (viii) ..+0= ..... The above examples shows that zero is an additive identity for integers . you can verify it by a adding zero to any other five integers . In general , for any integer a , a+0=0+a=a