The definition of increasing function given in my school maths text book is
Let I be an open interval contained in the domain of a real valued function f. Then f is said to be increasing on I if for all .
And a theorem given after it is
f is increasing in I if .
Shouldn't it be .
Is constant function an increasing function? Or a function like where at some or all points which are increasing according to definition.
Edit: The definition of decreasing function given is
f is decreasing on I if .
A constant function follow this definition too.