Increasing and decreasing functions - conflicting authors

I am starting to read Stewart's Calculus Early Transcendentals (1999 ed.)
for a Calc I class that will begin in a few weeks. In it he talks about
increasing and decreasing functions and shows the intervals using closed
interval notation. In my College Algebra text (Beecher, Penna, &
Bittinger), they emphatically state that you need to use open interval
notation when discussing increasing, decreasing, or constant intervals as it
is impossible for a point to be increasing and decreasing at the same time.

Tin the Algebra text they show a function that was increasing in the
interval (3,5) and decreasing over the interval (5, inf). Stewart shows a
similar situation. I do not have the book before me, but the gist of it is
a function that is increasing [3,5] and decreasing on [5,inf].

I suspect it is Stewart that is wrong here, but I am not sure. Can anyone
give me a definite answer as to whether such intervals need to be open or
closed?
Thanks.


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