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I don't really understand what is the importance of w in the homogeneous coordinate (x,y,z, w).

One of the example i have read is about a parrallel line extended to infinity, and both line would meet at w=0. But what is the difference between (x,y,z, 0.5) and (x,y,z, 0) ? Isn't how the distance(in perspective) between 2 points on both lines is determined by z? I mean the farther the closer they get, why do we still need w?