Actually, even mathematicians don't agree on the
wording here.
In analysis we commonly talk about monotonic
functions,
which can be either monotonically increasing ( x <=
y => f(x) <= f(y) )
or monotonically decreasing ( x <= y
=> f(x) >= f(y) ).
Since analysis deals with continuous entities, the
distinction of
nondecreasing vs. increasing is usually not important,
and thus not
worried about. However physicists tend to make the
distinction
by saying "nondecreasing".
In dealing with sequences, the distinction is almost
universally made
between nondecreasing ( x_n <= x_n+1) and
increasing (x_n < x_n+1)
although the European school prefers stressing the
difference
by using the word "strictly" instead.
To make things more confusing, in order theory (where
you would
expect the wording to be the tightest) the wording
used is
monotone (for "increasing") and antitone (for
"decreasing").
Of course there the distinction between nondecreasing
and increasing
is not important since the description is of a
(partial) order relation,
and if that relation includes equality as a special
case than
you get one variety, while if not you get the
other.
Y(J)S
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