X server
That section contains SOME useful information about X servers.
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What does :0.0 mean?
The :0.0 part of the DISPLAY variable denote the display and the screen of an X server.
The display is the first number and equals to a running instance of an X server. If it is using TCP/IP for communication it listens on port 6000 + display-number for connections. With local (UNIX domain sockets) it uses the socket /tmp/.X11-unix/Xdisplay-number
The screen denotes different output devices of the X server. You could start XWin.exe with two -screen options and would end up with two X11 windows. Each of them is a different screen. Other X servers open different screens for different monitors connected to the computer.
Cygwin/X supports different formats of the DISPLAY variable
:0.0 or unix:0.0 This names a local X server and the communication uses the UNIX domain sockets.
hostname:0.0 This names a remote X server and the communication uses the TCP/IP network.