# Meaning of math notation Xi ∈ {0,1}^|C|

What is the meaning of this? $$x_i \in \{0,1 \}^{|C|}$$

This is the paper I'm trying to read https://papers.nips.cc/paper/6321-retain-an-interpretable-predictive-model-for-healthcare-using-reverse-time-attention-mechanism.pdf

The notation is in page 2 right at the bottom right.

What would the output X look like? I know that Xi belongs to something, but i'm unsure what it would look like.

• $|C|$ denotes the cardinal of $C$, then $X_i$ is a binary sequence of length $n$ where $n$ is the cardinal of $C$. – nicomezi Aug 21 '19 at 6:37
• So for example if C is 5 the binary sequence for a random Xi would be something like { C1 ,C2, C3 , C4 ,C5 }? where in each index of this set it could eather be 0 or 1? – Brian Formento Aug 21 '19 at 6:44

The $$\tau=|C|$$ is a scalar, a positive integer denoting the number of variables (and is possibly equal to the cardinality of some set $$C$$ which does no matter to us here). Therefore $$y\in \{0,1\}^{|C|}$$ means all the vectors for which all the entries are binary, i.e.$$y\in \{0,1\}^{|C|}\iff y_i=\text{either 0 or 1}$$