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I am trying to make sense of this proof in my textbook and find myself confused by a few things. I will try to present my question in the order that they come to me as I read the passage:
0) When defining the set A, "f is bounded above on [a,x]", x serves as a...
I have a really bad math background, so sometimes I struggle with or am just a little slow with some algebraic things, while I can handle more abstract stuff fairly well.
Lately I've been running into certain types of problems in my algebra class which are proving to be time-consuming for me...
I am studying for an upcoming exam and am, to this end, re-reading my textbook at a slow rate to identify anything I'm not completely certain about. Linear algebra is very cumulative and proofs require a good understanding of all definitions. So I will post some questions (for which I seek...
Homework Statement
Suppose that f satisfies f(x+y) = f(x) + f(y), and that f is continuous at 0. Prove that f is continuous at a for all a.
Homework Equations
f(x+y) = f(x) + f(y)
Limit Definition
Continuity: f is continuous at a if the limit as x approaches a is the value of the...
Hi. I'm a first-year calculus student and I'm fairly behind with my work. The transition is tough and when i read my textbook, I don't fully absorb everything. I thought I would post an example problem whose solution I do not follow completely, since it is fairly important in the scope of...
Homework Statement
Let P_4(\mathbb{R}) be the vector space of real polynomials of degree less than or equal to 4.
Show that {{f \in P_4(\mathbb{R}):f(0)=f(1)=0}}
defines a subspace of V, and find a basis for this subspace.
The Attempt at a Solution
Since P_4(\mathbb{R}) is...
Hello everyone. I was going through my Linear Algebra Done Right textbook that threw me off. I hope this forum is appropriate for my inquiry; while there is no problem I'm trying to solve here, I don't know whether just asking for clarification would belong to the homework forum instead. If...