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 Jun 17 revised On norms for “more complicated objects” deleted 75 characters in body Jun 11 revised Can every definite integral be expressed as a combination of elementary functions? added 2 characters in body Jun 10 awarded Nice Answer Jun 10 revised Express 99 2/3% as a fraction? No calculator added 693 characters in body Jun 9 answered Express 99 2/3% as a fraction? No calculator Jun 9 comment Why is $e$ so special? Thinking aloud: the function $e^x$ has many interesting properties, e.g. if we consider the function $e^x$, then we find the derivate of $e^x$ is itself $e^x$. This is quite remarkable ! When $x=1$ we obtain $e^1=e$. $e^x$ is also strictly positive for all $x\in\mathbb{R}$. $e^x$ is also a transcendental function. Another remarkable formula involving $e^x$ is $e^{i\pi}+1=0$, where $i=\sqrt{-1}$. Jun 8 comment The value of $\int^{\pi/2}_0 \frac{\log(1+x\sin^2\theta)}{\sin^2\theta}d\theta$ Sorry my mistake - updated. Jun 8 revised The value of $\int^{\pi/2}_0 \frac{\log(1+x\sin^2\theta)}{\sin^2\theta}d\theta$ deleted 13 characters in body Jun 8 answered The value of $\int^{\pi/2}_0 \frac{\log(1+x\sin^2\theta)}{\sin^2\theta}d\theta$ Jun 2 comment Why do we assume the complex plane is curvey at infinity? @ Ollie Ford yes, I think that's what popped into my head, but mathematics needs to be rigorous, so this is just food for thought really ! Jun 2 comment Why do we assume the complex plane is curvey at infinity? Just a thought: Give me any point $z$ in the upper half complex plane and I can tell you that the semi-circular contour of radius $|z|+1$ encloses it. Rectangular regions can be constructed similarly. Jun 2 comment Extension of $|\cdot|_\infty$ on $\mathbb R$ to $\mathbb C$ I think this is related to Ostrowski's Theorem. Check out en.wikipedia.org/wiki/Ostrowski%27s_theorem "...any field, complete with respect to an archimedean absolute value, is (algebraically and topologically) isomorphic to either the real numbers or the complex numbers. This is sometimes also referred to as Ostrowski's theorem." Jun 1 accepted Name for norm with property $\|x+y\|=\|x\|+\|y\|$. Jun 1 comment Name for norm with property $\|x+y\|=\|x\|+\|y\|$. Obviously people are liking your answer, but could you please clarify: Are you saying such a norm is called a "trivial norm"? Jun 1 asked Name for norm with property $\|x+y\|=\|x\|+\|y\|$. May 31 comment How do I calculate this integral:$\int_{0}^{1}\ln^2 \left| \sqrt x-\sqrt{1-x} \right|dx$? I would split the domain to which $x$ belongs to describe positive and negative regions. That way you can dispose of the absolute value and simply evaluate a finite sum of integrals having no absolute values. May 27 accepted Multiplying two inequalities May 27 asked Multiplying two inequalities May 27 revised How should I self-study calculus? added 186 characters in body May 27 answered How should I self-study calculus?