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In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
In constructive mathematics, "not empty" and "inhabited" are not equivalent: every inhabited set is not empty but the converse is not always guaranteed; that is, in constructive mathematics, a set that is not empty (where by definition, "is empty" means that the statement () is true) might not have an inhabitant (which is an such that ).
[5] lg – common logarithm (log 10) or binary logarithm (log 2). LHS – left-hand side of an equation. Li – offset logarithmic integral function. li – logarithmic integral function or linearly independent. lim – limit of a sequence, or of a function. lim inf – limit inferior. lim sup – limit superior. LLN – law of large numbers.
These imprecise uses of the word regular are not to be confused with the notion of a regular topological space, which is rigorously defined. resp. (Respectively) A convention to shorten parallel expositions. "A (resp. B) [has some relationship to] X (resp. Y)" means that A [has some relationship to] X and also that B [has (the same ...
In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures.Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships existing among the representing objects y i conform, in some consistent way, to ...
The edge relation [note 1] of a tournament graph is always a connected relation on the set of ' s vertices. If a strongly connected relation is symmetric, it is the universal relation. A relation is strongly connected if, and only if, it is connected and reflexive. [proof 1]
In mathematics, a binary relation R ⊆ X×Y between two sets X and Y is total (or left total) if the source set X equals the domain {x : there is a y with xRy}. Conversely, R is called right total if Y equals the range {y : there is an x with xRy}. When f: X → Y is a function, the domain of f is all of X, hence f is a total relation.