1,558 reputation
411
bio website cse.iitb.ac.in/~aruniyer
location India
age 30
visits member for 2 years, 5 months
seen 16 mins ago

Jul
25
comment $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$
Your definition of f(x) should not contain that n.
Jul
23
comment Given $\{\log_ab \mid a,b\in \mathbb N, \mathrm{gcd}(a,b)=1,a,b≥3\}$ does the sum of any two $\log_ab$ form an irrational or rational number?
Try verifying the conditions for the group. Is it closed? Is it associative? Does it have an identity? What about inverses?
Jul
23
accepted What is a set function that returns another set of points called?
Jul
22
revised Prove that $\gcd(x, y)=\gcd(x,ax+y)$, would this be the correct reasoning?
Minor corrections.
Jul
22
suggested suggested edit on Prove that $\gcd(x, y)=\gcd(x,ax+y)$, would this be the correct reasoning?
Jul
22
comment What is a set function that returns another set of points called?
Actually, hmm scratch that, possibly m can be fixed. I will have to think about it. Thanks! I will upvote for the moment, will accept once I get some clarity on the situation myself.
Jul
22
comment What is a set function that returns another set of points called?
The reason I used the word set is because the size m of S is not necessarily fixed.
Jul
22
comment What is a set function that returns another set of points called?
The set-valued functions that I have come across don't seem to have set-valued input to the functions. I mean, the kind of set-valued functions studied seem to be $f:X\rightarrow 2^Y$ but not $f:2^X\rightarrow 2^Y$.
Jul
22
asked What is a set function that returns another set of points called?
Jul
21
comment If A is a balanced subset $\Longrightarrow$ conv$(A)$ is balanced
Your $C$ is not defined correctly. Define $C$ as $C = \{\sum_{i = 1}^{|A|}a_ix_i : a_i \geq 0 \forall i, \sum_{i = 1}^{|A|} a_i = 1, x_i \in A \forall i\}$. Proving that this is convex is very easy. You should also be able to show that this is equal to conv(A) very easily.
Jul
19
comment How to prove that $\frac{\sin \pi x}{\pi x}=\prod_{n=1}^{\infty}(1-\frac{x^2}{n^2})$
You should probably read this excellent article :-) cornellmath.wordpress.com/2007/07/13/…
Jul
16
comment What does a space mean?
@user50229 Thanks :-)
Jul
13
revised $F(u)= \frac{2}{\pi}\int_{0}^\infty \frac{uf(x)}{u^2 + x^2}dx.$ Show that $\lim\limits_{u\downarrow0}F(u)=f(0)$.
Fixed an error in the title
Jul
13
suggested suggested edit on $F(u)= \frac{2}{\pi}\int_{0}^\infty \frac{uf(x)}{u^2 + x^2}dx.$ Show that $\lim\limits_{u\downarrow0}F(u)=f(0)$.
Jul
9
comment approximation of the sum of matrices
You can show that $\|r_i \nabla^2r_i\| \leq \epsilon$. This would imply that $\|H - \tilde{H}\| \leq \epsilon$.
Jun
22
comment properties of two positive definite matrix
@miosaki you have already shown if A is positive definite then A^2 is positive definite. Similarly, B^2 is positive definite. Also, you know that if X and Y are positive definite, then X + Y is positive definite. If you put X as A^2 and Y as B^2, what do you get?
May
7
awarded  Caucus
Apr
23
awarded  Yearling
Mar
27
answered Why do we use gradient descent in the backpropagation algorithm?
Mar
21
comment norm of a linear operator
For a fixed $x$, $\|A(x)\| = \|A(\frac{x}{\|x\|})\| \|x\| \leq \|A\|\|x\|$. The first step uses linearity of the operator and the second step uses definition of the operator norm. This is not a complete proof, one has to consider some case, but the gist of the proof is just this much.