The phrase 'terminal multiplexer' sounds a bit of a mouthful and a large dollop of jargon. Multiplexing is a method of combining multiple data streams into one stream over a shared medium. This gives us a hint of the function of a terminal multiplexer. It is computer software that can be used to multiplex several video consoles. In English? Well, it allows you to make use of multiple separate terminal sessions inside a single terminal. So one terminal session can act like many sessions.
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