/sci/ - Science & Math

>>9757795
I have a question, I'd appreciate it if anyone could answer it or point me in a useful direction:
I'm looking at the space of all positive sequences of real numbers who's sum at infinity converges to a finite number.
On this space I define the inner product - the product of two sequences, is the sum of the sequence created by multiplying the two sequences together, term by term.
I also define the linear functional of a sequence as the sum of its corresponding series.
I'm trying to prove that this is an example of a linear functional that can't be represented as an inner product with some specific vector from this space (I.E, there is no series 'a' in our space such that for any series 'b' in our space, the functional can be represented as <b, a>.

Any help would be appreciated.

>>9615986
this is the science board, faggot

I have a question for the people here, I hope you'll have an answer for me:

I recently finished my first semester as a physics and math double major. While I really enjoyed my math courses, I couldn't relate to my course in mechanics at all. Even though we derived all of the formulas ourselves and everything, I still felt like nothing was rigorous enough and that we lacked the proper tools to really understand the formalism of what we're doing. I don't know, maybe the math classes just spoiled me and made used to everything being well defined and understood.
But my question is - does physics get better? Do things become more rigorous? Or is this just the general attitude all throughout the degree? (My uni is considered pretty good in physics so I don't think it's a problem with the university itself, maybe I'm wrong.)
I know that it's just a first class in mechanics, and that things will be more precise once we get to analytical mechanics, but I'm still afraid that I'll spend my whole degree waiting for some real rigor to happen, but it'll never happen.
Did anybody else go through something like this?

Hey guys, I'm looking for your opinion:
I'm building my class schedule for next semester (physics major) and I noticed that I have enough time to fit in another class, so I thought I might take up a course I'm not obligated to take (just to expand my horizons a bit).
Taking my preferences and class schedule into account, I decided that I'm either gonna take combinatorics or digital systems.
My question is - what course would you recommend out of the two? I'm not asking what's more practical or what's easier, but what do you think is more interesting (because like I said, this is strictly for pleasure). If you took one of the two (or both), please explain what exactly you enjoyed more and less about it, and what to what type of person you'd recommend such a class.
Thank in advance!

>>9380018
Where does that put chemical engineers?