- #36
FinalStand
- 60
- 0
I give up. Thanks for the help
What does "that" refer to? Do you mean that you already knew that F(ℝ) is defined that way? If so, why have you still not realized that the zero vector is a function?FinalStand said:I know that
I don't even know what this means. What is f? Are you saying that this holds for all f in F(ℝ)? Are you saying that there exists an f in F(ℝ) such that this holds? Is f some specific member of F(ℝ), and you're saying that this holds for that f? What do you mean by "add the x of the opposite sign"? What do you mean by "gives you 0"? What 0? The number or the vector?FinalStand said:but for f(x)=f(-x) can't we just add the x of the opposite sign then it givesyou 0?
You obviously need to rethink that strategy. It can't possibly work for very long.FinalStand said:And no I did not buy the textbook because I never needed textbooks for math..well until maybe now.
You seem to be fixated on this relatively minor point. What you appear to be doing is making random manipulations of this formula that describes which functions are in the set, without understanding what things are actually in the set. For example, is f(x) = x2 + x + 1/2 in W?FinalStand said:Could it be (f+(-f))(x)=0 then f(-x)+ (-f(-x))=0? Can you guys tell me what the answer is so maybe I can work it out?
Are you referring to my example of f(x) = x2 + x + 1/2? Why isn't it in the set? Show me your thinking.FinalStand said:no that is not in the set
Actually, g(x) = 1 IS in set W.FinalStand said:...for example 1 would not work.
FinalStand said:You guys kept on repeating the same thing and I do not understand that thing. I don't know any thing and I have no idea what thing you are talking about either. I think I need to go drop this course or drop myself down a building and suicide.
What does this have to do with anything? There is no requirement that an arbitrary member of set W has to touch the x-axis.FinalStand said:And it does not touch the x-axis therefore it will not work.
FinalStand said:But I still don't see the point of this. I think the examples and the definitions are irrelevant. So what if it says x+y=x then why do we still need to proof that it is in f(x)=f(-x) ? of course there is an x that f(x+y=x) = f(-x+y=-x) what is the point on giong over the definitions? And what's the point of proofing this? I think it is all rubbish. i gave up on math I will change my major then. Screw myself with a million screw drivers.
Mark44 said:Are you referring to my example of f(x) = x2 + x + 1/2? Why isn't it in the set? Show me your thinking.
Actually, g(x) = 1 IS in set W.
What does this have to do with anything? There is no requirement that an arbitrary member of set W has to touch the x-axis.
FinalStand said:WHy does that matter!? Why are we looking at examples? no the second one does not satisfy all x. it is not a vectorspace at all. :). But how does this matter? I want ot know how to proof that whether 0 is in the space or not.
So (f+0)(x)=f(x)+0(x)=f(x)=f(-x) work?
You don't seem very certain. micromass's question was this:FinalStand said:yes. f(x)+0(x) = f(-x) + 0(x)?
When f is defined by f(x)=0 for all x in ℝ, as in micromass's post, then yes, we have f(x)=f(-x) for all x. So the equality in the quote above holds. But I'm not sure how the conversation drifted into this.FinalStand said:yes. f(x)+0(x) = f(-x) + 0(x)?
Linear algebra is along with the basics of calculus the most important topic in mathematics. It's used extensively in all sorts of applications of mathematics from quantum mechanics to computer graphics. It's also used in other areas of mathematics. It's a foundation on which many other things are built.FinalStand said:...what is the point on giong over the definitions? And what's the point of proofing this? I think it is all rubbish.
f(x) is not a vector, it's a number in the range of the function f, which is a vector. f is called a vector because it's a member of a vector space.FinalStand said:I thought f(x) was the vector ? So do I have to say f(x) = 0 is the zero vector and belongs to the subspace since f(x)=f(-x)? I am not exactly sure how to answer this question. How is f a vector? I am so confused, this is so different from what we learned before I took this course. It is more abstract than I like it to be.
A subspace in linear algebra is a subset of a vector space that satisfies all the properties of a vector space. This means that it is closed under addition and scalar multiplication, contains the zero vector, and is closed under linear combinations. It is essentially a smaller vector space within a larger vector space.
To determine if a set is a subspace, you need to check if it satisfies the three properties of a vector space: closure under addition, closure under scalar multiplication, and contains the zero vector. If all three properties are satisfied, then the set is a subspace.
A subspace is a subset of a vector space that satisfies all the properties of a vector space, while a span is the set of all possible linear combinations of a given set of vectors. In other words, a subspace is a subset of a vector space, while a span is a set of vectors.
No, a subspace cannot be empty. It must contain at least the zero vector, as one of the properties of a subspace is that it contains the zero vector. If a set does not contain the zero vector, it cannot be a subspace.
Linear independence is a property of vectors in a vector space. If a set of vectors is linearly independent, it means that none of the vectors can be written as a linear combination of the other vectors in the set. This is important in determining if a set of vectors can form a basis for a subspace.