In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in K, and can be turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication.
In mathematics, more specifically in functional analysis, a Banach space (pronounced ˈbanax) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space. Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly.
A garden is a planned space, usually outdoors, set aside for the cultivation, display, and enjoyment of plants and other forms of nature. The single feature identifying even the wildest wild garden is control. The garden can incorporate both natural and artificial materials. Gardens often have design features including statuary, follies, pergolas, trellises, stumperies, dry creek beds, and water features such as fountains, ponds (with or without fish), waterfalls or creeks.