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Apr
25
comment Showing a recursively defined sequence is convergent
@Dave Isn't that exactly what OP tries?
Apr
25
answered Showing a recursively defined sequence is convergent
Apr
25
awarded  Nice Answer
Apr
25
comment Direct Proof for sum of $n$ integers equation?
+1 for invoking WWGD
Apr
25
answered Construct a turing machine that accepts L = {ww : w belongs to {a,b}*}
Apr
25
answered A problem in group theory_dsom
Apr
25
answered Fourier series: can a function be odd and have a dc component?
Apr
25
answered Polynomial division proof
Apr
25
comment If $\lim_{x\rightarrow\infty}f(x)=0$, does $||f||_{L^2}=0$?
Then how dare you write $\to$ after the fixed norm of a fixed function?
Apr
25
comment Show that There exists a canonical injective homomorphism between $G$ and $G\times H$
Note that "canonical" more or less means that the solution is nearly impossible not to find. - So you are given an element $x\in G$ and nothing special from $H$. Which element $(g;h)$ of $G\times H$ could you write down with those givens and without knowing anything more detailed about $G$ and $H$? Well, $g$ must be an element of $G$ and we are given an element $x$ of $G$, so ... And $h$ must be an elemtn of $H$ and the only element of $H$ that wwe know to exist is ...
Apr
25
answered Using the axiom of choice to choose bijections
Apr
25
comment Why doesn't L'Hospital's rule work for this limit?
The rule (for this particular indeterminate form) says: If $f(x)\to \infty$ and $g(x)\to \infty$ and $\lim\frac{f'(x)}{g'(x)}$ exists, then $\lim\frac{f'x)}{g(x)}$ exists and equals $\lim\frac{f'(x)}{g'(x)}$.
Apr
25
comment The sum of two numbers is 5/9…
I read the last instruction as asking for $(0.4 x)\cdot (0.4y)$
Apr
25
answered Does there exist a complex function which is differentiable at one point and nowhere else continuous?
Apr
25
comment Has the polynomial distinct roots? How can I prove it?
@drxy I found my counterexample by just playing around with $\gcd(f,f')$, motivated by mathguy's solution for real roots. I'm sure that playing around will also allow finding counterexamples (regarding complex roots) for higher $p$ values one by one - but the handling becomes impractical.
Apr
25
comment Prisoners and hats variation
Do they guess only once? OR is the game repeted (with the same hats) if nobody dared to guess?
Apr
25
comment $\sup\limits_{t>0}[\frac{g(t)}{\sup\limits_{t<u<\infty}g(u)}]\leq 1$
To fleshen out the last sentence: Replace $2^{-n}$ with $\frac1{n!}$
Apr
25
answered How can I show that $G$ is non abelian of order 20?
Apr
25
answered You are given two points and a circle. Construct a circle passing through the given two points and tangent to the given circle.
Apr
25
comment $\frac{0}{0}$ Indeterminate
The notion "indeterminate form" relates to the fact that $a_n\to 0$, $b_n\to 0$ does not tell us much about the limit of $\frac{a_n}{b_n}$. Howver, $\frac 00$ is also "undefined" for the simple reason that it is not immediately defined per the usual definition of $\frac ab$ as the unique solution (if it exists) of $b\cdot x=a$. Lacking uniqueness in the case $a=b=0$, this definition does not cover $\frac 00$. -- In contrast to this, $0^0$ is an "indeterminate form" (in the unkown-limit-sense above), but it is defined (contrary to somewhat popular belief)