In mathematics, a set is called finite if the number of its elements can be described by a natural number. For instance, the set of integers between -15 and 3 is finite, since it has 17 elements. The set of all prime numbers is not finite. Sets that are not finite are called infinite.
In physics, the term finite is in addition used in the meaning of "non-zero", for instance in a sentence like "if the distance of the two objects is finite...".
... not optimal
[0,1,4,6] optimal
[1,2,4,8,16,..(powers of 2)..] not optimal
References:
Martin Gardner, "Mathematical games", Scientific American, March 1972, p. ...