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Aug
12
answered Does limit exist for the following expression?
Aug
11
comment Area between the curve and x-axis
Hi stuart, I see you have already asked a few questions, most of which have received good answers. If you're satisfied with an answer, you can not only upvote it, but also accept it by using the little check mark right below the up- and downvote arrows. This lets whoever answered your question know that you are indeed satisfied with the answer, and it helps people spot questions which still need more attention. :)
Aug
11
revised Area under a curve subintervals
added 34 characters in body
Aug
11
revised Area under a curve subintervals
added 20 characters in body
Aug
11
answered Area under a curve subintervals
Aug
11
comment Differential geometry: $|\alpha(t)|=c\ne 0 \iff \langle \alpha(t),\alpha'(t)\rangle = 0,\forall t\in I$
Yes, both summands on the LHS of your equation are equal because of symmetry of the inner product, so they must both be zero. You can basically go along the exact same chain of thought - but backwards - to get the other direction of the statement you want to prove.
Aug
11
answered Differential geometry: $|\alpha(t)|=c\ne 0 \iff \langle \alpha(t),\alpha'(t)\rangle = 0,\forall t\in I$
Aug
11
comment Linear map with polynomials - Find a matrix
That's correct. And what does a linear combination of the elements of the set $\{1,x,x^2,x^3\}$ look like?
Aug
11
comment Linear map with polynomials - Find a matrix
Do you see that $P_3$ is a vector space? Do you know what the definition of a basis of a vector space is? Can you write a general expression that every element in $P_3$ looks like?
Aug
10
comment Linear map with polynomials - Find a matrix
Do you know why $\{1,x,x^2,x^3\}$ is a basis of $P_3$? The strategy you use to find $A$ is usually the same: You apply $F$ on your basis and then see which matrix $A$ satisfies $A \cdot v = F(v)$ for all $v$ in your vector space. The matrix corresponding to a linear map depends on a basis - thus if you take a different basis in ii), you will have a different matrix $A'$. My answer here might be helpful: math.stackexchange.com/a/1087851/3787
Aug
10
awarded  Civic Duty
Aug
7
comment English translation of von Neumann's “Zur Theorie der Gesellschaftsspiele”, 1928
I'm afraid I can't since I haven't read it myself. My game theory course was in German, so we used German books/articles. Are you just interested in learning some basic game theory in general or do you absolutely want to read about it from Von Neumann?
Aug
7
answered English translation of von Neumann's “Zur Theorie der Gesellschaftsspiele”, 1928
Aug
7
comment Multiplications in determinant of an $n \times n$ matrix?
If you don't know what the notation $\mathcal{O}(N^3)$ means, check out this: en.wikipedia.org/wiki/Big_O_notation
Aug
7
comment Example of a nowhere dense subset of a metric space.
What's the closure of $\mathbb{Z}$? What's its interior?
Aug
7
comment How did Euler give a sum to the divergent series $…x^{-3}+x^{-2}+x^{-1}+1+x^1+x^2+x^3.. = 0$?
How is this supposed to hold for any $x > 0$? All summands are strictly positive, so their sum surely can't be $0$?
Aug
5
comment Jänich linear algebra, Question 2.3 solution clarification
Take $U_1 = U_2 = \{0\}$. Is $(U_1 \cup U_2) \setminus U_2 = U_1$?
Aug
5
answered Explanation of this integral's solution
Aug
3
accepted Proving that the coordinate basis is a basis of a tangent space
Aug
3
comment What is the difference between the following $2$ sets?
What is the difference between $[1+\delta, \infty)$ and $(1,\infty)$? Does one of them contain the other?