The additive identity is a unique element of a set which has the property that adding it to any element of the set leaves the value of that element unchanged. The identity is normally denoted by 0.
That is: for any X in the set, X + 0 = 0 + X = X
Whether or not the set is commutative, addition of the identity always is.
The additive inverse of one element of a set is a member of the set (not necessarily different nor unique) such that the sum of the two is the additive identity. The additive inverse of an element X is normally denoted by -X.
Thus, X + (-X) = (-X) + X = 0
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They have no real relations ofther than being mathmatical properties The additive identity states that any number + 0 is still that number; a+0 = a The additive inverse property states that any number added to its inverse/opposite is zero; a + -a = 0
There are two related identity properties: the additive identity and the multiplicative identity. The additive identity property states that for x belonging to a set, there is an additive inverse in the set, which is denoted by -x such that x + (-x) = (-x) + x = 0, where 0 is the additive identity which also belongs to the set. The multiplicative identity property states that for y belonging to a set, there is a multiplicative inverse in the set, which is denoted by 1/y or y-1 such that y * (1/y) = (1/y) + y = 1, where 1 is the multiplicative identity which also belongs to the set.
It is the number 0. The identity property allows you to solve equations. If you want to remove a term from one side of an equation to add its additive inverse to both sides.
additive inverse is when in an equation there is a plus zero. you automatically know that anything plus 0 is still that number, so that is additive identity.
The additive inverse means what undoes adding. The additive inverse of +1 is -1.