celtschk
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 Oct 24 comment Why can't you square both sides of an equation? @Manishearth: He did gain a solution: He started from an equation with zero solutions ($\sqrt{x}=-3$) and arrived at an equation with one solution ($x=9$). Which solution do you think he lost? Oct 24 comment Why can't you square both sides of an equation? You don't have to invoke $f^{-1}$: The definition of "injective" is $f(a)=f(b)\implies a=b$, no intermediate step required. Oct 19 comment If $|f(x)+g(x)|=|f(x)|+|g(x)|$ and $|f(x)|=\lambda |g(x)|$ do we have $f(x)=\lambda g(x)$? The first condition is definitely< not sufficient, as it is fulfilled for every pair of non-negative functions, even if they are not constant multiples of each other, say $e^x$ and $e^{2x}$. Note that the absolute value is not a norm on the space of functions; rather it maps functions to other functions. Oct 19 comment Inequality of complex numbers Hint: What is $(1-\left|z\right|)(1-\left|w\right|)$? Oct 19 comment How to solve $xyy'' − 2x(y')^2 + yy' = 0$ I would divide by $y^2$, and then notice that it can be rewritten in terms of $y'/y$ and its derivative. Oct 18 comment Square root of continued fraction That doesn't answer my question. Note that the question is in the first paragraph; there's a reason the second paragraph begins with "For example". Oct 18 revised Square root of continued fraction edited tags; edited tags Oct 18 asked Square root of continued fraction Oct 12 comment Let $T:\mathcal{P}(\mathbb{R})\to \mathcal{P}(\mathbb{R})$ such that $T(p)=p-p'$. Find all eigen values and eigen vectors of $T$. Ah, I understand, you interpret "$p'$" as "derivative of $p$". I interpreted it as some constant value independent of $p$ that is also a polynomial. Which shows how important it is to properly specify the problem. :-) Oct 12 comment Let $T:\mathcal{P}(\mathbb{R})\to \mathcal{P}(\mathbb{R})$ such that $T(p)=p-p'$. Find all eigen values and eigen vectors of $T$. I don't see anything stating a specific degree of $p'$. Oct 12 comment Let $T:\mathcal{P}(\mathbb{R})\to \mathcal{P}(\mathbb{R})$ such that $T(p)=p-p'$. Find all eigen values and eigen vectors of $T$. What about $p=\alpha p'$? Oct 11 awarded Inquisitive Oct 10 comment Two spaces contain the same vector, can we say the space with smaller dimension is a subspace of the larger one? @peter: See edit Oct 10 revised Two spaces contain the same vector, can we say the space with smaller dimension is a subspace of the larger one? edited to make all entries of alpha and beta positive Oct 10 answered Two spaces contain the same vector, can we say the space with smaller dimension is a subspace of the larger one? Oct 10 comment What is the right way to define a function? Oct 10 accepted Deriving topology from sequence convergence/limits? Oct 10 asked Deriving topology from sequence convergence/limits? Oct 10 comment Greatest integer less than or equal to $x^*$ I guess some of your $x^*$ should have been just $x$. Oct 10 comment On the proof that for $0 a$ (for example, $x = \left(\frac{1+a}{2}\right)^{1/n}$). Thus an $a$ that doesn't depend on $x$ cannot be found in that case.