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

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

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)?

$$[m]$$ is not the variable $$m$$, but is instead the set of integers from $$1$$ to $$m$$ inclusive. The empirical error equation thus reads in English:
The cardinality of a set consisting of the elements $$i$$ of the set of integers $$[m]$$ such that the hypothesis given input $$x_i$$ disagrees with label $$y_i$$, normalized by $$m$$.