(1) The system whose life cycle is under consideration. (ISO/IEC/IEEE 2008)
(2) The system of interest to an observer. (Bertalanffy 1968)
(1) ISO/IEC/IEEE. 2008. Systems and Software Engineering - System Life Cycle Processes. Geneva, Switzerland: International Organization for Standardization (ISO)/International Electrotechnical Commission (IEC), Institute of Electrical and Electronics Engineers. ISO/IEC/IEEE 15288:2008 (E). The second definition is an expanded version of the ISO/IEC/IEEE version.
(2) von Bertalanffy, L. 1968. General system theory: Foundations, development, applications, revised ed. New York, NY: Braziller.
(1) Is the common Systems Engineering definition. A system-of-interest is a collective set of all elements of any system considered by a lifecycle, this may include both operational or enabling systems. Strictly this definition is relevant for an engineered system of interest.
(2) Is the system science definition and applies to all systems irrespective of whether they have a purpose or lifecycle in an engineering sense.
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