/sci/ - Science & Math

it's false, u just try to figure out why

OP

I'm thinking Span{x} as a line through the origin, which doesn't necessarily mean the x vector EQUALS the zero vector, it just contains it?

Can any mathfags confirm this???

>>1773000
AHAHAHAHAHAHA. no.

>>1772972
This is linear algebra, specifically talking about sets. The span is the set of all power sets of x. Since that is then x, x must be 0 (the empty set).

Span of x = ax, the only case where it is only x is if x = 0

o forgot to say, its true

It's true. Every field has at least 2 elements 0 and 1, thus every vector space has at least 2 elements. Span{x} = {ax | a is in F}.

If Span{x} = x, then we know that 0*x is in Span{x} and 1*x is in Span{x} since every field contains 0 and 1, and so we have 0*x = 1*x which implies that 0 = x by the axioms of a vector space.

>>1773010
you are retarded lol, and you don't udnerstand set theory

>>1773021
We haven't learned about vector spaces yet and so I have no idea what you are talking about

>>1773021
>since every field contains 0 and 1, and so we have 0*x = 1*x which implies that 0 = x by the axioms of a vector space.

you had me until there

How can it equal 0 if the subspace is non-empty?

>>1773063
because the only vector in the subspace is 0

>>1773039
One of the axioms states that 1*x = x for all x in the vector space.

Also, 0*x = (0+0)*x = 0*x + 0*x => 0*x = 0 for all x in the vector space.

Every field has a unique additive identity called 0, and a unique multiplicative identity called 1.

So since Span{x} = {x} and Span{x} = {a*x | a is in F} => 0*x is in Span{x} and 1*x is in Span{x}, so then 1*x = 0*x but 1*x = x and 0*x = 0 implies that 0 = x.

Or, you could argue that Span{x} is a subspace of the vector space and since a subspace must contain the 0 vector, that means that since x is the only element in Span{x} that x is the zero vector.

Span{x} = equis

>>1773073
explain further?

>>1773077
>Or, you could argue that Span{x} is a subspace of the vector space and since a subspace must contain the 0 vector, that means that since x is the only element in Span{x} that x is the zero vector.

That's what I was thinking...the problem was that I assumed the Statement to be false because I forgot if P is always true then Q is true as well.

FFFFFUUUUUUU

Thanks though

>>1773086
The only subspace with 1 vector in it is the 0 vector so x = 0.
>>1773077
>>1773021
explained it properly