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First of all, it was difficult to find the proper title for my question. Basically, I would like to write an equation for the following:

For each branch $b_i$ where i in 1 to n, the BEC value for that branch is

$$\sum_{l=1}^{w} r_l \ \forall \ r_l \in \left \{ 0, 1 \right \}$$

where w is the number of runs and $r_l$ is whether the branch $b_i$ has been executed in that run (i.e., = 1) or not (i.e., = 0).

To write that as an equation, I did the following:

$$\forall \ b_i \ where \ i \in \left \{ 1, \dots, n \right \} BEC_i = \sum_{l=1}^{w} r_l \ \forall \ r_l \in \left \{ 0, 1 \right \}$$

I'm not quite sure if this equation looks fine or not.

Can someone please help me in writing the proper equation?

Nasser
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1 Answers1

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If you're writing for computer science, you can use $[1..n]$ for set notation and "such that" (s.t.) instead of where:

$\forall b_i$ s.t. $i \in [1..n] : $ ...

I would also rearrange the equation so that the quantifier is placed ahead of the sum:

$\forall b_i$ s.t. $i \in [1..n] : \forall r_l \in \{0, 1\} : BEC_i = \sum_{l=1}^w r_l $

Some computer scientists use colon to specify the domain, and dot to separate the statements: $\forall b_i: i \in [1..n] \cdot \forall r_l: r_l \in \{0, 1\} \cdot BEC_i = \sum_{l=1}^w r_l $

Alternatively, the quantifiers can be merged.

$\forall b_i, r_l \cdot BEC_i = \sum_{l=1}^w r_l$, such that $i \in [1..n], r_l \in \{0,1\}$

V S
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