diff --git a/Doc/library/resource.rst b/Doc/library/resource.rst
--- a/Doc/library/resource.rst
+++ b/Doc/library/resource.rst
@@ -52,11 +52,13 @@
 
    Sets new limits of consumption of *resource*. The *limits* argument must be a
    tuple ``(soft, hard)`` of two integers describing the new limits. A value of
-   ``-1`` can be used to specify the maximum possible upper limit.
+   ``-1`` can be used to request a limit that is infinite/unlimited.
 
    Raises :exc:`ValueError` if an invalid resource is specified, if the new soft
    limit exceeds the hard limit, or if a process tries to raise its hard limit
-   (unless the process has an effective UID of super-user).  Can also raise
+   (unless the process has an effective UID of super-user).  Specifying an
+   infinite/unlmited limit when the hard or system limit for that resource not
+   unlimited will result in a :exc:`ValueError`.  ``setrlimit`` may also raise
    :exc:`error` if the underlying system call fails.
 
 These symbols define resources whose consumption can be controlled using the