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-) I use downvotes to organize answers to a question. By voting up I bring up the answers that I consider more important, useful, or that I think should be read first. By voting down I also do the same. If I downvoted your answer, it might not be that I think it is bad, but that I think other answers should be on top of yours in the list.

I think that this, together with bounties, is the only way to put those banal reputation points to good use.

-) Being arrogant or a snob are for me the worst qualities there are. If I see arrogance or snobbery I will try to find my chance to crush you, if I can. I am specially infuriated when I see a beginner that is trying to learn mathematics being mistreated.

-) Homework is not necessarily for you to do alone. You should work on it a little, with all your strength if possible, but ultimately seeing the problem statement and seeing answers of it are what is most important from a homework. All people do in math is to combine what they have seen someone do before; from the student to the best of the scholars. That is why it is important for students to see things being done. You will always get exams in which your ability to work alone is going to be tested. Homework is not the ideal teaching resource for that. It is your job to make sure you are prepared for working alone. Meanwhile, bring your homework problems if you want to see their solutions. If I see it, I will answer it, if I can, even if it is in the narrow space of the comments.


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Mar
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comment Sequence solving need help.
You can do $\frac{\sqrt{n}}{n\sqrt{n}-(n-1)\sqrt{n-1}}=\frac{\sqrt{n}(n^{3/2}+(n-1)^{3/2})}‌​{(n^{3/2}-(n-1)^{3/2})(n^{3/2}+(n-1)^{3/2})}=\frac{\sqrt{n}(n^{3/2}+(n-1)^{3/2})}‌​{(n^{3}-(n-1)^{3})}=\frac{n^{1/2}(n^{3/2}+(n-1)^{3/2})}{-3n^2+3n-1}$.
Mar
30
revised Sequence solving need help.
added 10 characters in body
Mar
30
comment the continuous functions with norm
Maybe not, but notice that a continuous function with $\lim_{|x|\rightarrow\infty}f(x)=0$ will necessarily have $||f||_\infty<\infty$.
Mar
30
comment the continuous functions with norm
$||f||_\infty$ denotes $\sup_{\mathbb{R}} |f|$. It is usually taken as a norm in $C(\mathbb{R})$.
Mar
29
comment To Find $A^{50}$
@ketan That is long division of polynomials.
Mar
29
comment Why are these expressions indeterminate expressions?
The reason why it doesn't work is because one can find examples: $f(x)=1/x$, $g(x)=x^k$. In which $\lim f(x)g(x)$ depends in what the functions $f$ and $g$ actually are, and not only on $\lim f(x)$, and $\lim g(x)$.
Mar
29
comment Why are these expressions indeterminate expressions?
Let us only look to $0\cdot \infty$. The formula that it is referring to is $\lim f(x)g(g)=\lim f(x)\lim g(x)$. But the formula only works under certain restrictions. One of them is if $\lim f(x)=0$ and $\lim g(x)=\infty$.
Mar
29
comment Why are these expressions indeterminate expressions?
They are mnemonic formulas to remember the cases in which the formulas that describe how the limit operation behaves with respect to the arithmetic operations, do not work.
Mar
29
revised Why are these expressions indeterminate expressions?
added 5 characters in body; edited title
Mar
29
comment Matrices and what they represent
The usual multiplication of matrices is done with a purpose. When $f$ and $g$ are linear transformations, and $A$ and $B$ are their matrices. The definition of matrix multiplication is done such that the matrix of $f\circ g$ is $AB$ and the matrix of $f+g$ is $A+B$. Often in courses one sees the operation being defined ad hoc, for the sake of the exposition. For example, usually matrices and their operations are studied before linear transformations are studied.
Mar
29
comment Matrices and what they represent
When the matrix is used to represent a linear transformation, one calls it the matrix of the linear transformation in certain bases. The bases should be part of the name because the matrix representation of the data depends on those bases.
Mar
29
comment Matrices and what they represent
Then, depending on the use, one makes up operations of the matrix that imitate operations on the data they represent. For example componentwise addition and matrix multiplication, are defined when one is using the matrix to represent a linear transformation. This is done such that, when one adds or multiply matrices, that corresponds to what happens when one adds or compose linear transformations. If one changes to other uses of a matrix, for example in an image filter, the multiplication that might be useful could be componentwise.
Mar
29
comment Matrices and what they represent
Matrix is just a table to contain something, some information. It comes from a Latin word that means womb. You maybe referring to some applications of these tables to represent linear transformation, for example. But they are also used for many other purposes. Representing graphs, data, images, points, data of any sort.
Mar
29
comment Sequence of $a_n=(-\frac{1}{2})^n$
The positive terms are $(-\frac{1}{2})^{2n}=(\frac{1}{4})^n$. Similarly for the negative terms.
Mar
29
revised Sequence of $a_n=(-\frac{1}{2})^n$
edited body; edited title
Mar
29
revised Help with this problem please
added 21 characters in body
Mar
29
comment Find extension of $\mathbb{Q}$ containing components of eigenvectors of a matrix
Yes, and finding a primitive element, $a$, for that extension. Notice the part about constructing such an element. There you see also an example. If the characteristic polynomial is $(x^2-2)(x^2-3)$, then $a$ is not really any of its roots. One needs to take, for example, $a=\sqrt{2}+\sqrt{3}$.