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 Dec 15 comment Image of unit sphere being hyper ellipse proof (SVD) @littleO it was a pretty good proof, thank you :) Dec 15 comment Image of unit sphere being hyper ellipse proof (SVD) @littleO should not it have a standalone proof as well? Also are we talking about this proof?: cs.cornell.edu/courses/cs322/2008sp/stuff/… Nov 24 comment Problem related to Complex and linear mappings @PaulSinclair Ok now I solved the first part, $K$ should be $$\begin{bmatrix}A & 0\\0 & A\end{bmatrix}$$. Do you have an idea about the second part? Nov 23 comment Problem related to Complex and linear mappings @EmilioNovati I edited the question, now everything should be fine I hope Oct 27 comment Reflection through a hyperplane, orthogonality propoerty Check out the second part of the first question: web.stanford.edu/class/cs205/homework/hw2_solutions.pdf Oct 5 comment Proof of $\Pr(A\mid B)\ge (a+b-1)/b$ Negation of less than or equal to should be only greater than? Oct 15 comment How many 6 digit numbers with 2 or 3 repetitions allowed @calculus sorry for my bad English. I modified the question, maybe this time it is simpler to understand. From 2 repetitions, I tried to mean that every digit (0,..,9) can be used at most 2 times while forming the 6 digit number. Oct 15 comment How many 6 digit numbers with 2 or 3 repetitions allowed @CameronBuie yes both of them are true for their cases. sorry for the late reply Apr 8 comment Combinatorial explanation to following recurrence relation $a_n = 2 a_{n-1} + a_{n-2}$ @xen I did not say azimut's proof is not combinatorial. I just wanted to say it may not be what Xentius looking for according to his previous questions. But of course only one to confirm this is Xentius. Apr 8 comment Combinatorial explanation to following recurrence relation $a_n = 2 a_{n-1} + a_{n-2}$ I guess what @Xentius meant by a combinatorial proof is not this. He seems to be looking for an answer like in this question he asked: math.stackexchange.com/questions/340905/… Mar 19 comment Binomial formula for $(x+1)^{1/3}$ (related to Newton's binomial theorem) @Xentius it's called gamma function. Dec 16 comment Proof about diameter of a set I guess this should be enough for a) Choose $x_n ∈ A_n$ , and show that the sequence $(x_n)$ satisfies the Cauchy condition. Dec 5 comment Limit proof of $a^n$ where |a|<1 yeah it is so simple. how could not I think that! :/ I guess I need to take a rest. thank you for your answer. Dec 5 comment Limit proof of $a^n$ where |a|<1 @nikita2 you are right. I edited my question. Dec 3 comment Boundary and Interior Points of the set: Rational Numbers @TonyK Oh I guess I understood what you wanted to say. In the interval $(X_0-r,X_0+r)$, there are also irrational numbers and therefore it cannot be a subset of $Q$. Right? Nov 30 comment Using Euler Phi function to show that there are infinitely many primes I guess I understood why $\phi(m) = 1$. Any selection of (m,n) will not be relatively prime only (m,1) will be relatively prime hence $\phi(m) = 1$. That is brilliant. Thank you so much. Nov 30 comment Using Euler Phi function to show that there are infinitely many primes I guess it must go on like this: we know that $\phi(m) = 1$ however according to the multiplicative property of the phi function, $\phi(m) = (p_1-1)*(p_2-1)*...*(p_k-1)$ which is not clearly equal to 1. However I could not exactly understand why $\phi(m) = 1$. Maybe I should give it some time. = ) Nov 26 comment Infinitely number of primes in the form 4n+1 proof @GerryMyerson can you show me a way to prove it? Nov 26 comment Showing that if a subset of a complete metric space is closed, it is also complete was that all? :D Nov 26 comment Showing that if a subset of a complete metric space is closed, it is also complete I am extremely tired so that it has become really hard to think clear, but I added more details about what I have done so far. Could you please take a look and help me to put this proof in a correct shape? Thanks!