interleave sequence

Let $S$ be a set, and let $\{x_i\},i=0,1,2,\mathrm{\dots }$ and $\{y_i\},i=0,1,2,\mathrm{\dots }$ be two sequences in $S$. The interleave sequence is defined to be the sequence $x_0,y_0,x_1,y_1,\mathrm{\dots }$. Formally, it is the sequence $\{z_i\},i=0,1,2,\mathrm{\dots }$ given by