In mathematics, a monotonic function sequence is a special function sequence of real-valued functions . A function sequence is called monotonically increasing if the function values for each argument form a monotonically increasing sequence and monotonically decreasing if they form a monotonically decreasing sequence. Monotonic function sequences are one of the many monotonic terms in mathematics and can be viewed as a special case of monotonic mapping .
Are for real-valued functions, then the sequence of functions is called
monotonically increasing on , when all is
monotonously noticeable when is for everyone , and
monotonic if it is either monotonically decreasing or monotonically increasing.
example
Consider the sequence of functions as an example . she is
falling monotonously , since it is equivalent to and
since in is always for and is always less than zero for . The sequence of functions is thus also monotonous .
increasing monotonically , since then is always greater than 1 and the term is always positive, i.e. is
.
The sequence of functions is thus also monotonous . However, it is not monotonous because it has no clear monotony behavior on this larger interval, but only on the smaller sub-intervals and .
not monotonous . It is always positive, but it is
.
Thus, changes to the signs of the time, it can therefore apply no monotony.