The least period of a periodic function, periodic sequence, or periodic point is the smallest positive period allowed in the corresponding setting, when such a minimum exists.
For a periodic function 
of a real variable, the least
period is the smallest real number 
satisfying
 |
(1)
|
for all real numbers 
. It is also called the fundamental period (Adkins and Davidson
2016, p. 725). For example, the sine and cosine
functions have least period 
. A constant function
has every positive real number as a period,
so it has no least period.
For a periodic sequence 
, the least period is the smallest positive
integer 
satisfying
 |
(2)
|
for every index 
.
The term fundamental period is also used in this setting (Ellis 2007, p. 38).
For example, the sequence 1, 2, 1, 2, 1, 2, ... has
least period 2. A sequence whose terms are all equal
has least period 1.
For a periodic point 
of a function 
, the least period is the smallest positive
integer 
satisfying
 |
(3)
|
where 
denotes 
-fold
iteration. In this setting, the least period is also
called the exact period. For the function 
, every nonzero point has
least period 2, whereas 
has least period 1.
