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I'm looking for the correct way to define a sum of all elements in a set that fullfill a certain condition.

Example: $$ n(A) = \frac{\sum_{F \in A}{ \begin{cases} A_F\text{ is }\mathrm{NULL} & w_F\\ \text{else} & 0 \end{cases}}}{\sum_{F \in A}{w_F}} $$

A is to supposed to be a record with a number of fields $F$. $A_F$ is the value of field F in the record A. $w_F$ is a weight associated with the Field $F$. I want to calculate how much percent of the record is NULL weighted according to $w_F$.

What I want to know is if this below is a valid way to formulate this or if there is a better way.

If someone has some pointers on a more formal / mathematical notation for database/records I would also be very grateful.

Thanks!

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2 Answers 2

up vote 3 down vote accepted

Although I don't think it is quite mainstream, but you could look into Iverson Notation. In short, you have a bracket and inside you write a condition. The bracket value is 1 if the condition holds, otherwise it's 0. Its most popular usage was in Concrete Mathematics (by Knuth et al).

$$ n(A) = \frac{\sum_{F \in A}{w_F[A_F \neq NULL]}}{\sum_{F \in A}{w_F}} $$

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I like this one. Looks very natural. I think I will go for this notation at least for the moment and hope that it's common enough for my professor to recognize it ;-) –  aKzenT Jan 15 '12 at 20:06

For the sake of clarity, I would describe such an operation with the help of a short sentence. Also, it is quite common to put some summation conditions in the index spot of the sum symbol, as in

$$\sum_{p \text{ prime}} 1/p$$

In my opinion, it is best to describe what you have written above as

(Brief description of what kinds of objects $A$, $w_F$, $A_f$, etc are and a quick name for what $n(A)$ describes)

$$n(A) = \sum_{F \in A, A_F = 0} w_F/\sum_{F \in A}w_F$$

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I thought about this one, but I would like the condition to be a bit more visible instead of putting it only in the subscript of the sum. The formula is inside a larger text explaining the operation in text also, just like I did above. –  aKzenT Jan 15 '12 at 20:04

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