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[5] [6] [7] This is complicated by a lack of knowledge of the characteristics of living entities, if any, that may have developed outside Earth. [ 8 ] [ 9 ] Philosophical definitions of life have also been put forward, with similar difficulties on how to distinguish living things from the non-living. [ 10 ]
As another example, consider the positive integers, ordered by divisibility: 1 is a least element, as it divides all other elements; on the other hand this poset does not have a greatest element. This partially ordered set does not even have any maximal elements, since any g divides for instance 2 g , which is distinct from it, so g is not maximal.
A presentation on information flow in living systems. Living systems are life forms (or, more colloquially known as living things) treated as a system. They are said to be open self-organizing and said to interact with their environment. These systems are maintained by flows of information, energy and matter. Multiple theories of living systems ...
For example, the ideal completion of a given partial order P is the set of all ideals of P ordered by subset inclusion. This construction yields the free dcpo generated by P . An ideal is principal if and only if it is compact in the ideal completion, so the original poset can be recovered as the sub-poset consisting of compact elements.
In mathematics, the poset topology associated to a poset (S, ≤) is the Alexandrov topology (open sets are upper sets) on the poset of finite chains of (S, ≤), ordered by inclusion. Let V be a set of vertices. An abstract simplicial complex Δ is a set of finite sets of vertices, known as faces , such that
A living thing may be an object, and is distinguished from non-living things by the designation of the latter as inanimate objects. Inanimate objects generally lack the capacity or desire to undertake actions, although humans in some cultures may tend to attribute such characteristics to non-living things.
The classification of living things into animals and plants is an ancient one. Aristotle (384–322 BC) classified animal species in his History of Animals, while his pupil Theophrastus (c. 371 –c. 287 BC) wrote a parallel work, the Historia Plantarum, on plants. [7]
An organism is any living thing that functions as an individual. [1] Such a definition raises more problems than it solves, not least because the concept of an individual is also difficult. Many criteria, few of them widely accepted, have been proposed to define what an organism is.