How do we denote the $0$ vector in a Quotient Space $V /W$?

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Just $0$ or $0 + W$? Unfortunately my textbook has no mention of the notation for this, nor can I find clarification for this online.

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I think the most standard way to write it is just $0$, but you can also call it $0 + W$ or $[0]$. There is no fixed notation in this sense: Different books use different notations.