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Understanding What does the notation $[m]=\{1, \ldots, m\}$ mean in the equation of the empirical error?

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understanding how to compute Understanding the equation of the empirical error equation

The empirical error equation given in the book 'Understanding machine language: from theory to algorithms'Understanding Machine Learning: From Theory to Algorithms is

enter image description here

My intuition for this equation is: total wrong predictions divided by the total number of samples m$m$ in the given sample set S$S$ (Correct me if I'm wrong). But, in this equation, the m$m$ takes {1,....,m}$\{ 1, \dots, m \}$. How is this actually calculated, as I thought it should be one number (the size of the sample)?

understanding how to compute empirical error equation

The empirical error equation given in the book 'Understanding machine language: from theory to algorithms' is

enter image description here

My intuition for this equation is: total wrong predictions divided by total number of samples m in the given sample set S (Correct me if I'm wrong). But in this equation the m takes {1,....,m}. How is this actually calculated as I thought it should be one number (the size of the sample)?

Understanding the equation of the empirical error

The empirical error equation given in the book Understanding Machine Learning: From Theory to Algorithms is

enter image description here

My intuition for this equation is: total wrong predictions divided by the total number of samples $m$ in the given sample set $S$ (Correct me if I'm wrong). But, in this equation, the $m$ takes $\{ 1, \dots, m \}$. How is this actually calculated, as I thought it should be one number (the size of the sample)?

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understanding how to compute empirical error equation

The empirical error equation given in the book 'Understanding machine language: from theory to algorithms' is

enter image description here

My intuition for this equation is: total wrong predictions divided by total number of samples m in the given sample set S (Correct me if I'm wrong). But in this equation the m takes {1,....,m}. How is this actually calculated as I thought it should be one number (the size of the sample)?