monotonically decreasing

A sequence $(s_{n})$ is monotonically decreasing if

s_{m}<s_{n}\\;\\forall\\;m>n

Similarly, a real function $f(x)$ is monotonically decreasing if

f(x)<f(y)\\;\\forall\\;x>y

Compare this to monotonically nonincreasing.

Conflict note. In other context, such as [1], this is called strictly decreasing. When this is the case, “monotonically nonincreasing” is instead called “monotonically decreasing.”

References

1 “http://www.nist.gov/dads/HTML/strictlyDecreasing.htmlstrictly decreasing,” from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.