Yes. Those would be numbers such as 5 and -5, which only have opposite signs - they are called additive inverses (of one another).
Usually, the identity of addition property is defined to be an axiom (which only specifies the existence of zero, not uniqueness), and the zero property of multiplication is a consequence of existence of zero, existence of an additive inverse, distributivity of multiplication over addition and associativity of addition. Proof of 0 * a = 0: 0 * a = (0 + 0) * a [additive identity] 0 * a = 0 * a + 0 * a [distributivity of multiplication over addition] 0 * a + (-(0 * a)) = (0 * a + 0 * a) + (-(0 * a)) [existence of additive inverse] 0 = (0 * a + 0 * a) + (-(0 * a)) [property of additive inverses] 0 = 0 * a + (0 * a + (-(0 * a))) [associativity of addition] 0 = 0 * a + 0 [property of additive inverses] 0 = 0 * a [additive identity] A similar proof works for a * 0 = 0 (with the other distributive law if commutativity of multiplication is not assumed).
If you mean the ADDITIVE INVERSE, change the minus sign to a plus sign. (And if you see a plus sign, you change it to a minus sign.)
The opposite is defined in the context of an operation. So, if the operation is addition, then the opposite is the additive inverse. If the operation in multiplication, then the opposite is the reciprocal. If the operation is exponentiation then the opposite is the logarithm, if the operation is sine then the opposite is arc sine. In function notation, if y = f(x) then the opposite is x = f-1(y), which may or may not always be defined.
I assume you mean the additive inverse. The sum of any number and its additive inverse is zero. For example, 7 + (-7) = 0.
The additive inverse is +4
Two integers which sum to zero (e.g. 3 and -3) are additive inverses of each other. All pairs of additive inverses sum to 0 and all pairs of integers which sum to 0 are additive inverses.
They are pair of additive inverses or additive opposites.
No. It has a different additive inverses for each element.
The answer depends on the context. There are opposite numbers that can be the additive inverses, or multiplicative inverses.
Additive inverses or additive opposites.
They are called the additive inverses!
They are additive inverses.