Computer software

What is a computer? – Computer software

A computer* is an inanimate device that has no intelligence of its own and must be supplied with instructions* so that it knows what to do and how and when to do it. Colloquially, the totality of these instructions are called software.* The importance of software can't be overestimated. You might have what most people consider the "best" computer sitting on your desk in front of you; however, without software to "feed" it, the computer will do nothing more than take up space.
    Software is made up of a group of related programs,* each of which consists of a given set of instructions or statements that perform very specific processing* tasks. Software can generally be divided into three categories: systems software, applications software,* and software development tools.
    The systems software called the operating system consists of programs designed to function as the principal interface between all the hardware* and software components, the currently running application programs, and the user(s) of the computer. In many ways, systems software functions in the same way as a business manager who tells and instructs the "hardware" and "software" components of the business what to do and how and when to do it while coordinating complex business tasks, and communicating with the "external" actors of business life. Applications software is a collection of related programs designed primarily to be carried out by a computer to satisfy the users' specific needs. Those programs are usually created by software development tools.

In general, software refers to a certain set of computer programs that can be executed by a computer system. Specifically, the actual or running software of a computer system consists of a system of mutually cooperating programs, including e.g.

A computer program is a sequence of instructions or statements that can be executed by the computer in a well-defined order so as to produce a desired output by processing the input and the stored data.

In general, the terms 'algorithm' and 'operation' are closely related to the mathematical concept of the function. Particularly, an operation is a function from the m-ary Cartesian product SxSx...xS into S itself, where 'm' is a natural number (usually 1 or 2, called a unary or binary operation, respectively), and 'S' is some set specific to the function.

Here, the term Cartesian product is central. The Cartesian product or cross product is a set of ordered n-tuples the elements of which are respectively members of the sequence of given sets. For example, the Cartesian product AxBxC is the set of all triples (a,b,c) where 'a' is a member or element of the set 'A', 'b' is a member of 'B', and 'c' is a member of 'C'. (Note that if the sets A, B and C are finite, and the number of elements of the sets are |A|=q, |B|=r, and |C|=s, respectively, then there are exactly q*r*s triples in the Cartesian product AxBxC.)

Boda István, 2023.