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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