Comparable
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Comparable
Comparable may refer to: * Comparability, in mathematics * Comparative In general linguistics, the comparative is a syntactic construction that serves to express a comparison between two (or more) entities or groups of entities in quality or degree - see also comparison (grammar) for an overview of comparison, as wel ..., in grammar, a word that denotes the degree by which an entity has a property greater or less in extent than another See also * Incomparable (other) {{disambig ...
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Comparability
In mathematics, two elements ''x'' and ''y'' of a set ''P'' are said to be comparable with respect to a binary relation ≤ if at least one of ''x'' ≤ ''y'' or ''y'' ≤ ''x'' is true. They are called incomparable if they are not comparable. Rigorous definition A binary relation on a set P is by definition any subset R of P \times P. Given x, y \in P, x R y is written if and only if (x, y) \in R, in which case x is said to be to y by R. An element x \in P is said to be , or (), to an element y \in P if x R y or y R x. Often, a symbol indicating comparison, such as \,,\, \geq, and many others) is used instead of R, in which case x < y is written in place of x R y, which is why the term "comparable" is used. Comparability with respect to R induces a canonical binary relation on P; specifically, the induced by R is defined to be the set of all pairs (x, y) \in P \times P such that x i ...
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Comparative
In general linguistics, the comparative is a syntactic construction that serves to express a comparison between two (or more) entities or groups of entities in quality or degree - see also comparison (grammar) for an overview of comparison, as well as positive and superlative degrees of comparison. The syntax of comparative constructions is poorly understood due to the complexity of the data. In particular, the comparative frequently occurs with independent mechanisms of syntax such as coordination (linguistics), coordination and forms of Ellipsis (linguistics), ellipsis (gapping, pseudogapping, null complement anaphora, Stripping (linguistics), stripping, verb phrase ellipsis). The interaction of the various mechanisms complicates the analysis. Absolute and null forms A number of fixed expressions use a comparative form where no comparison is being asserted, such as ''higher education'' or ''younger generation''. These comparatives can be called ''absolute''. Similarly, a null ...
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