Minimum notation of modified set elements analog to Sum notation

Question

I'm currently trying to simplify a calculation that takes the minimum of all elements in a set. However the elements should not be taken as they are but be modifiable:

$$ S = \{{A}, {B}, {C}\}\\ min(({f}_{A} \cdot {m}_{A}), ({f}_{B} \cdot {m}_{B}), ({f}_{C} \cdot {m}_{C})) $$

Is there any way to write this shorter for all elements, if it was a sum not a minimum it would be some like this:

$$ \sum\limits_{x \in S}^x {f}_{x} \cdot {m}_{x} $$

Thanks for your help!

score 3 · Accepted Answer · answered Aug 23 '13 at 12:23

3

A common way to write this would be $$\min_{x\in S}\{f_x\cdot m_x\}$$ Or sometimes with $()$ instead of $\{\}$.

answered Aug 23 '13 at 12:23

Tobias Kildetoft

21,247

2

Sometimes also: $$\min{f_x\cdot m_x\mid x\in S}$$ – Tomas Aug 23 '13 at 12:25
Thank you very much! I think I'll go with the sub-notation as it reminds me of the sum notation. – Thomas Fankhauser Aug 23 '13 at 13:04

Minimum notation of modified set elements analog to Sum notation

1 Answers1