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Dec
30
comment Determining the basis of a span of vectors for all values of $a$.
$(a, 1, 1)$ and $(1,a,1)$ are the basis of what they span. (They are linearly independent and they span the vectorspace.) Do you want an orthonormal basis of something?
Dec
30
revised Is it possible to find $\angle BOA$?
added 112 characters in body
Dec
30
answered Is it possible to find $\angle BOA$?
Dec
30
revised Proving the limit
Corrected, it should be $O(1/x^2)$ and not $O(x^2)$.
Dec
28
comment What if the intermediate point is $c=(0,0)$ in the MVT?
Right - I missed that. But in that case we know the $\nabla f(0,0)$ has to be the only value that can maintain continuity of $\nabla f$ around the origin, i.e. it has to be $(0, 1)$.
Dec
28
answered What if the intermediate point is $c=(0,0)$ in the MVT?
Dec
28
answered Finding $f(x)$ such that $\int_{a}^{b}f(x)dx=\sum_{k=a}^{b}f(k)$
Dec
28
comment Sum of $\sum\frac{1}{i^{i}}$
Edit: OP is interested in $\sum_{k=1}^\infty k^{-k}$.
Dec
28
answered Proving the limit
Dec
28
revised Let $a > 1$ be a real number and $n > 1$ be a positive integer. Prove that $a^n-1 > n\left(a^{\frac{n+1}{2}}-a^{\frac{n-1}{2}}\right)$.
deleted 82 characters in body
Dec
28
comment Let $a > 1$ be a real number and $n > 1$ be a positive integer. Prove that $a^n-1 > n\left(a^{\frac{n+1}{2}}-a^{\frac{n-1}{2}}\right)$.
You're right. Edited.
Dec
28
answered Let $a > 1$ be a real number and $n > 1$ be a positive integer. Prove that $a^n-1 > n\left(a^{\frac{n+1}{2}}-a^{\frac{n-1}{2}}\right)$.
Dec
28
comment How can I count solutions to $x_1 + \ldots + x_n = N$?
Agreed. The WLOG needs to be explained more... though this might be in a right direction.
Dec
28
comment Find if two multi-dimensional parallelograms intersect
Yes that's exactly how I did it, used a LP solver. Notice this problem is simpler than a full LP, since all I am interested in is if the feasible region is non-empty. Also there are some nice symmetries. I was wondering if there is any direct way to solve this problem.
Dec
28
accepted Find if two multi-dimensional parallelograms intersect
Dec
23
awarded  Tumbleweed
Dec
16
asked Find if two multi-dimensional parallelograms intersect
Sep
9
awarded  Stellar Question
Aug
18
awarded  Yearling
Jul
5
comment Taking the square root of an imaginary number
That the field of real achieves algebraic closure with introduction of only one element is remarkable and deserves emphasis. It is not in genral true. For example to close the field of rationals you need to add infinitely many numbers.