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I have created a set notation in which I am uncertain whether this is formally correct or not. It is about the set of all indices of the data points that fulfill a certain equation:

$\mathbb{S} = \{i \; | \; y^{(i)}(\beta^{T} \cdot x^{(i)} + b) -1 = 0 \;, \forall i = 1,...,M\}$

The question is if the 'i' in the left part of the set actually refers to the indices or if I have to formulate it differently?

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    $\begingroup$ It does not make sense to define a set of all indices $i$ such that for all $i$ some condition is satisfied. $\endgroup$
    – Paul Frost
    Commented Jul 5, 2019 at 9:29

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$\mathbb{S} = \{i \; | \; y^{(i)}(\beta^{T} \cdot x^{(i)} + b) -1 = 0 \;, i \in \{ 1,...,M\}\}$
corrects your mistake.

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  • $\begingroup$ Thank you. One more question, just out of curiosity does the order matter in the 'right / conditional' part of the set? Strictly speaking the 'i`s' are not defined in the equation if their definition comes in the second place? $\endgroup$
    – xvzwx
    Commented Jul 5, 2019 at 9:51
  • $\begingroup$ And another question: If I would write the set as $\mathbb{S} = \{x \; | y^{(i)}...=0 \;, i \in \{1,...,M\} \}$ would it still refer to the indices, or does it matter to specifically choose (in this case) the letter 'i' in order to refer to them? $\endgroup$
    – xvzwx
    Commented Jul 5, 2019 at 9:58
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    $\begingroup$ It is a set of x's. @xvzwx $\endgroup$ Commented Jul 5, 2019 at 12:14
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    $\begingroup$ {1,2,.. M} is unordered. $\endgroup$ Commented Jul 5, 2019 at 12:15

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