# Does zero vector only exist in dim 0?

Hi,

just curious, is it false to say the vector 0 exists in R^n, n>0 and a natural number?
i.e. does x = [0, 0, 0, 0] exist in R^4, or simply the zero space?
My guess is that the first statement is not false given that the zero space is a subspace of R^n, n>0.

Am I right or wrong?

Thanks

## Answers and Replies

The zero vector is the additive identity; it exists in all Rn, and is defined as $<0, 0, ... , 0>$.

EDIT: My statement is misleading. "The zero vector" does not exist in every Rn; rather, for every n, there exists an element of Rn which is the additive identity and is called the zero vector.

HallsofIvy