FFT implementation using Danielson-Lanczos Lemma I am trying to understand FFT algorithm explained here

FFT(x) {   n=length(x);   
if (n==1) return x;   
m = n/2;   
X = (x_{2j})_{j=0}^{m-1};   
Y = (x_{2j+1})_{j=0}^{m-1};  
X = FFT(X);   
Y = FFT(Y);  
U = (X_{k mod m})_{k=0}^{n-1};   
V = (g^{-k}Y_{k mod m})_{k=0}^{n-1};   
return U+V; 
} 


The author says that the above comes from Danielson-Lanczos Lemma. 

I am unable to understand what is the meaning of the lines:

X = (x_{2j})_{j=0}^{m-1}; 

Y = (x_{2j+1})_{j=0}^{m-1};
The meaning of the first line is "Let $X$ be an array of length $m$ (with indices running from $0$ to $m-1$) such that $X_j = x_{2j}$ for $j \in \{0,\ldots,m-1\}$." The second line has a similar meaning, with $Y_j = x_{2j+1}$ instead.