2017年6月14日 · Note that the minimum is not always well-defined. For example, given the interval $(0,1)$, there is no smallest element in the interval, since we may find numbers in the interval arbitrarily close to zero.

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$\begingroup$ Note that a set being infinite certainly does not mean that $\min$ becomes invalid. Consider for example the natural numbers, which certainly have a least element. Consider for example the natural numbers, which certainly have a least element.

2018年8月14日 · $\begingroup$ The subscript of $\min$ is often used to denote the set in which the minimization takes place. For example $\min_{x\in[0,1]}(f(x))$ is the same as $\min(\{f(x):\ x\in[0,1]\})$.

Express max/min with conditions? Hot Network Questions How (in)efficient would a rocket be that flew to orbital heights, hovered for a while, and then fell back down instead of going into orbit and back?

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If you want a symmetric expression, you can take $\frac13 (\min(a,\min(b,c))+\min(b,\min(a,c))+\min(c,\min(a,b)))$. But if you rewrite it using that absolute-value trick, I still don't think it gives something that's "intuitively the minimum", I'm afraid...

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2015年9月16日 · "Let a,x,y be elements of R. If a < min(x,y) then a < x and a < y" The above is a theorem that I encountered in my Real Analysis course. I do not want to ask about what it means, but rather concerning the "min(x,y)" being used. The nature of it I am not clear about, even after a conversation with my lecturer about it.