>>9713586>The answer is no, but I am wondering why this is the case, since the zero vector satisfies this property, and the zero vector is a subspace with dim of R^0.firstly, it sounds like you are confusing two things: the zero vector and the zero vector .
the zero vector is an element of every vector space, which has the property that 0+x=x for any x in the space. the zero vector space, {0}, is a vector space consisting only of the zero vector.
though i think you probably know that
now let V be a vector space. for a subset of V to be a subspace it needs a zero vector, but this isnt the only requirement. the set must also be closed under the vector addition and scalar multiplication operations from V.
from this you can see the zero vector space is a subspace of vector space; however, having a zero vector does not in general make a set a subspace (because of the last sentence).
in your particular question, the set is not a subspace. although it has a zero vector, it is not closed under vector addition or scalar multiplication. to see this take .
but . hence U is not closed under +. therefore is not a subspace.
>>9714129i think it is up to your discretion how the x values are placed relative to each other. i think most importantly you need to figure out what x measures. i've not played that game, but i assume what is on the x axis currently are sort of upgrades (better chips as x increases) for the weapons. if you think each upgrade is "worth" the same amount, then your x values will all be equally spaced. if you think the "higher up" chips give a better advantage, then they will further apart than the "lower" chips. dont know if that helps you.
