Final answer:
The property you're asking about is the Additive Identity Property. It states that the sum of any number and 0 is the number itself. The null vector in vector algebra is the equivalent concept where the null vector added to any other vector does not change the original vector.
Step-by-step explanation:
The property in algebra that adds up to 0 is known as the Additive Identity Property. This property states that for any number a, the sum of a and 0 is a itself (a + 0 = a). Similarly, the Additive Inverse Property ensures that for every number a, there exists a number -a such that a + (-a) = 0. The number -a is known as the additive inverse of a. In vector algebra, the null vector serves a similar role, where every component of the null vector is zero, and when added to any vector, it leaves the original vector unchanged.