### Proving V is a subspace of W - My Math Professor

This quote was added by user91542
If it is given that V is a subset of a vector space W, then showing that V is a subspace means we must only verify vector space properties three and four for V. That is to say, V must contain the zero vector, and a negative vector for each vector in V. All other vector space properties are implied by the fact that V is a subset of W.

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##### mathnerd8 months, 1 week ago
Unfortunately, this is wrong. What you probably meant is that for all v, w ∈ V, we have v - w ∈ V. What you wrote is not enough. For example, take V = {0, 1, -1} as a subset of say ℚ (regarded as a vector space over itself).

Also the terminology "negative vector" is slightly imprecise. Better to say "opposite".

Finally, saying "properties 3 and 4" doesn't really make much sense. I guess those refer to your textbook, but the numbering is not universal, so most people wouldn't know which properties you're talking about.
##### bagdat20048 months, 1 week ago
random math lesson amid typing practice absolutely loved it
Hell yeah.
wuut?

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