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Thats why i ask. "the socket library" is an very odd way to refer to the libc.

Some other Unix operating systems had the functions in a own socket library, e.g. SunOS: https://docs.oracle.com/cd/E19120-01/open.solaris/817-4415/s... .

I suppose though in the context of Linux it's a bit weird, but you did get the correct meaning :).

Not in context.