Deos this question make sense to anyone?

[Emspak]

OK Let me see if I get this: the issue is that you're defining V (the vector space) from the get-go as the set of functions that are non zero at one point only. If you can put two functions together in that space V it isn't a vector space anymore. But if it isn't just one point then it's ok, it is still a vector space. As I understand it this starts <i>from the definition of V itself</i>.

(BTW I also discovered earlier this evening that the original problem as I presented it was wrong because the prof who wrote the assignment had a huge typo, the "real" problem was to prove a set was as subspace. Oh lord.)

Anyhow I think what was confusing me was that I got hung up on what functions do when you've already defined a space that they are in rather differently. In vector calculus for instance you don't get into the properties that make a vector space a vector space.

And I want to thank you for your patience. There are aspects of this that are really frustrating at first. I am not trying ot be flip or go off tangentwise, I was sort of following some reasoning in the text.

 

[Dick]

OK Let me see if I get this: the issue is that you're defining V (the vector space) from the get-go as the set of functions that are non zero at one point only. If you can put two functions together in that space V it isn't a vector space anymore. But if it isn't just one point then it's ok, it is still a vector space. As I understand it this starts <i>from the definition of V itself</i>.

(BTW I also discovered earlier this evening that the original problem as I presented it was wrong because the prof who wrote the assignment had a huge typo, the "real" problem was to prove a set was as subspace. Oh lord.)

Anyhow I think what was confusing me was that I got hung up on what functions do when you've already defined a space that they are in rather differently. In vector calculus for instance you don't get into the properties that make a vector space a vector space.

And I want to thank you for your patience. There are aspects of this that are really frustrating at first. I am not trying ot be flip or go off tangentwise, I was sort of following some reasoning in the text.

Proving it's a subspace of a vector space is certainly easier. You don't have to prove all of the axioms. Given the axioms are true for the larger space means most of them are automatically true for the subset. You just have to prove the closure ones. But it's not horribly different. And, no, in vector calculus you don't have to worry about whether it is a vector space. That's sort of implicit in the subject. This is more abstract. But do you see the difference between "at most one" and "a finite number" I was trying to spell out?

 

[Emspak]

Well, I see that if the set is defined in the first place as being that which only has functions that are nonzero at one point, and further reduce that (by definition) to only one. if you have any other functions that are zero then you aren't in the set anymore. Yes?

 

[Dick]

Well, I see that if the set is defined in the first place as being that which only has functions that are nonzero at one point, and further reduce that (by definition) to only one. if you have any other functions that are zero then you aren't in the set anymore. Yes?

I hope that means the same thing I tried to explain, it's not a very clear statement.