Recent content by freshlikeuhh

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    Unclear About Proof

    http://i.imgur.com/uhqc5.jpg 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...
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    Tips For Algebraic Manipulation

    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...
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    Basic Linear Algebra Questions

    Thank you very much for the reply. It has certainly cleared things up for me. Oops. Seems like I got it backwards. But polynomials can be thought of as functions; so for a polynomial of finite dimension, does it make sense to think of it as a list of functions?
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    Basic Linear Algebra Questions

    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...
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    Continuity Problem

    Well, I understand how the property f(x+y)=f(x)+f(y) is used to demonstrate f(0)=0 and obviously it is employed to expand f(a+h)=f(a)+f(h). I understand that this step is supposed to demonstrate the continuity of all a, but then why is h->0, and how exactly is continuity of a demonstrated if a...
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    Continuity Problem

    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...
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    Applying the Limit Definition

    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...
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    Basis for Polynomial Subspace

    Ohh. I think I follow; by plugging in for a, the elements we obtained form a basis? That is, in each case of {(x2-x), (x3-x), (x4-x)}, 0 and 1 are roots: e.g., x2-x = x(x-1).
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    Basis for Polynomial Subspace

    Thanks for the quick reply, btw. I think I catch your meaning. That means the coefficients must sum to 0, for every element in the subspace(?). Given your helpful reply, I don't feel inclined anymore to fix x(x-1) as an element. That is, the fact that 0 is a root follows from there being...
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    Basis for Polynomial Subspace

    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...
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    Linear Independence: Polynomial Example

    Ah, that makes it all clear now. Thanks!
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    Linear Independence: Polynomial Example

    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...
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