Emanuele Paolini
Reputation
14,486
Top tag
Next privilege 15,000 Rep.
Protect questions
 Nov 8 comment Change of variables problem. The image seems to be not related to the question. Is it? Nov 8 answered Help with summation: $\sum_{k=1}^\infty\frac{k(k+2)}{15^k}$ Nov 8 comment Non-uniqueness of solutions of an ordinary differential equation This is a gap in many courses. I have seen books which write that the solution to $x'=2\sqrt x, x(0)=0$ is $x=t^2$. Which is not only inaccurate but completely wrong for $t<0$. Nov 8 revised Non-uniqueness of solutions of an ordinary differential equation deleted 1 character in body Nov 8 answered What is the limit of $\frac{a + (n-1)d}{2a + 2(n-1)d}$ for $n \to \infty$? Nov 8 answered Non-uniqueness of solutions of an ordinary differential equation Nov 7 comment Prove that $F_n < 2^n$ for every $n \geq 0$ - Mathematical induction Proving $P(n)\Rightarrow P(n+1)$ for all $n\ge 1$ is the same as proving $P(n-1)\Rightarrow P(n)$ for all $n\ge 2$. Nov 7 answered Notation for a set $\{a_1,a_2,a_3,a_4\}$, $a_i \in \{0,1\}$ for $i = 1,2,3,4$? Nov 7 comment Prove that $F_n < 2^n$ for every $n \geq 0$ - Mathematical induction what you have written is correct. You have proved that $F_n < 2^n$ for $n\ge 2$. Why do you feel that the usual definition is something different? Nov 6 revised Applications of the formula expressing roots of a general cubic polynomial deleted 3 characters in body Nov 6 asked Applications of the formula expressing roots of a general cubic polynomial Nov 3 comment Prove the function $f(x) = (a*x)^{-1}$ is bijective Taking the inverse of both sides you get: $a*x = a*y$... This is elementary algebra, like when you want to simplify the equation $1/(7x) = 1/(7y)$. Nov 2 revised Representation of an Abelian Lie algebra english Oct 30 comment Prove the function $f(x) = (a*x)^{-1}$ is bijective The inverse of $(a*x)^{-1}$ is $a*x$. Oct 30 answered Prove the function $f(x) = (a*x)^{-1}$ is bijective Oct 30 comment Proving a subset of a metric space is bounded You should mention what is the definition of bounded, since what you are asked to prove could be a definition. Oct 26 comment The mathematics underlying Rubik's games Oct 26 revised Help with proving property of Rubik's cube. added 67 characters in body Oct 26 answered Help with proving property of Rubik's cube. Oct 26 comment Sobolev embedding theorem, inequalities Maybe you can take $p=+\infty$ if $n<3$...