How can I determine which quantity is larger. $n$ an integer, $K$ and $F$ are reals and $x^{+} = \max( x , 0)$ :
$$n\left( -K + \frac{1}{n}\sum_{i=1}^{n} F_{i} \right )^{+}$$ compared to $$ \sum_{i=1}^{n} (-K + F_{i} ) ^{+}$$
Which quantity is larger
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real-analysis
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1What do you mean by the "+" exponent, and what is the relationship with linear algebra ? – 2017-02-27
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0the positive part. Yes I guess it's a wrong tag. – 2017-02-27
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0positive part of x= max(x,0) ? – 2017-02-27
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0I just edited the post. right – 2017-02-27
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0Can anyone explain this downvote ? – 2017-02-27
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1@YvesDaoust It was mine, and I removed it as the post got better. Still, the tag doesn't seem right. – 2017-02-27
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1Clearer to write $\left(\sum_{i=1}^{n}(-K+F_{i})\right )^{+}$, I guess. – 2017-02-27
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0@YvesDaoust No, I really meant $\sum_{i=1}^{n} (-K + F_{i} ) ^{+}$ – 2017-02-27
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0@RayGil It was meant instead of the _first_ expression. – 2017-02-27
1 Answers
2
Consider $G_i:=F_i-K$.
The first expresssion is the sum of all $G_i$, or zero.
The second is the sum of all positive $G_i$, hence not smaller than the above.