is a "non-decreasing" sequence "increasing"?

While studying the book "Introduction to Algorithms by Cormen", I found a strange thing. Everywhere if it refers to an increasing order, the book refers it as "non-decreasing" order.. I mean, if a series (2,5,6,3) is to be arranged in "non-decreasing" order.. is'nt it already right?? or "increasing" and "non-decreasing" words mean one and the same?

Increasing - 1 2 3 4

Nondecreasing - 1 1 2 3

The difference being that in an increasing sequence, for x(n) and x(n+1), x(n+1) > x(n) whereas in a non-decreasing sequence, x(n+1) >= x(n)

1,2,3,4 is an increasing sequence or a non-decreasing sequence.

1,1,1,1 is a non-decreasing sequence but isn't an increasing sequence.

Yes,

Monotonically Increasing == Increasing == Non-Decreasing

if f(a) >= f(b) for all a > b

Strictly Increasing Function :

if f(a) > f(b) for all a > b