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 May27 accepted Multiplying two inequalities May27 asked Multiplying two inequalities May27 revised How should I self-study calculus? added 186 characters in body May27 answered How should I self-study calculus? May26 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 $b\mid a$... May26 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 $D_1$. May23 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... May23 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? May22 accepted A name for the property $\| x \star y \| = \| x \| \| y \|$. May19 comment Curious formula for minimum? Thanks. I knew that must be true since they are clearly equal. May19 accepted Curious formula for minimum? May19 revised Curious formula for minimum? added 81 characters in body May18 comment A name for the property $\| x \star y \| = \| x \| \| y \|$. @tampis of course I should have remembered that from Number Theory ! May18 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! May18 revised A name for the property $\| x \star y \| = \| x \| \| y \|$. added 16 characters in body May18 asked A name for the property $\| x \star y \| = \| x \| \| y \|$. May18 revised Curious formula for minimum? added 144 characters in body May18 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. May18 accepted What does $O\left(\frac{1}{\log\log T}\right)$ mean? May18 asked Curious formula for minimum?