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The examples "is greater than", "is at least as great as", and "is equal to" are transitive relations on various sets. As are the set of real numbers or the set of natural numbers: whenever x > y and y > z, then also x > z whenever x ≥ y and y ≥ z, then also x ≥ z whenever x = y and y = z, then also x = z. More examples of transitive ...
The identity element of this operation is the empty relation. For example, ≤ is the union of < and =, and ≥ is the union of > and =. Intersection [e] If R and S are relations over X then R ∩ S = { (x, y) | xRy and xSy} is the intersection relation of R and S. The identity element of this operation is the universal relation.
An operational taxonomic unit (OTU) is an operational definition used to classify groups of closely related individuals.The term was originally introduced in 1963 by Robert R. Sokal and Peter H. A. Sneath in the context of numerical taxonomy, where an "operational taxonomic unit" is simply the group of organisms currently being studied. [1]
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces.
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The concept of "reciprocal altruism", as introduced by Trivers, suggests that altruism, defined as an act of helping another individual while incurring some cost for this act, could have evolved since it might be beneficial to incur this cost if there is a chance of being in a reverse situation where the individual who was helped before may perform an altruistic act towards the individual who ...
The black walnut secretes a chemical from its roots that harms neighboring plants, an example of competitive antagonism.. In ecology, a biological interaction is the effect that a pair of organisms living together in a community have on each other.