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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?
See en.wikipedia.org/wiki/…
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 $0<x<1$ there exists a real number $a$ s.t. $x^n < a$
But for any $a\in (0,1)$ and any $n$ you will find an $x$ so that $x^n > a$ (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.