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May
27
accepted Multiplying two inequalities
May
27
asked Multiplying two inequalities
May
27
revised How should I self-study calculus?
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May
27
answered How should I self-study calculus?
May
26
comment For which values of $\alpha$ does $ x^2+xy+y^2 = \left(\frac{x+y}{3}+1\right)^\alpha$ have a solution in integers?
Just some workings that may or may not lead to something useful: Take logarithms, $$\alpha\log\left(\frac{x+y}{3}+1\right)=\log(x^2+xy+y^2)$$ so that $$\alpha=\frac{\log(x^2+xy+y^2)}{\log\left(\frac{x+y}{3}+1\right)}.$$ Hence, you need $$x^2+xy+y^2=e^a$$ and $$\frac{x+y}{3}+1=e^b$$ such that $b\mid a$...
May
26
comment Rouché's Theorem for $p(z)=z^7-5z^3+12$
I may be wrong, but is your conclusion correct: $p(z)$ has $7$ roots in $D_2=\{z\in\mathbb{C}\mid |z|<2\}$ ? From your statement of Rouche's theorem you should conclude only that $p(z)$ has $0$ roots in $D_1$ since $f(z)=12$ has $0$ roots in $D_1$.
May
23
comment Is there an object in reality that is proven to be uncountable?
you could travel around the Earth countably infinite number of times, with certain unrealistic assumptions. That doesn't really answer your question but may be helpful to a layperson to understand you can pair off each circumnavigation with the natural numbers...
May
23
comment $\int _{ 0 }^{ 1 }{ \frac { { x }^{ t }-1 }{ \ln { x } } dx } $
What is $t$? An integer, rational, real, complex, ... Also, what have you tried so far?
May
22
accepted A name for the property $ \| x \star y \| = \| x \| \| y \| $.
May
19
comment Curious formula for minimum?
Thanks. I knew that must be true since they are clearly equal.
May
19
accepted Curious formula for minimum?
May
19
revised Curious formula for minimum?
added 81 characters in body
May
18
comment A name for the property $ \| x \star y \| = \| x \| \| y \| $.
@tampis of course I should have remembered that from Number Theory !
May
18
comment A name for the property $ \| x \star y \| = \| x \| \| y \| $.
Thanks both, wasn't sure about terminology. I will take a look into algebras!
May
18
revised A name for the property $ \| x \star y \| = \| x \| \| y \| $.
added 16 characters in body
May
18
asked A name for the property $ \| x \star y \| = \| x \| \| y \| $.
May
18
revised Curious formula for minimum?
added 144 characters in body
May
18
comment Curious formula for minimum?
@Andre I wasn't aware of the softmax function. Seems then that softmax can be transformed into the usual max by adding $-\log(1+e^{|x-y|})$ to it. Interesting.
May
18
accepted What does $O\left(\frac{1}{\log\log T}\right)$ mean?
May
18
asked Curious formula for minimum?