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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 ...
An example in modern English is the verb to arrive. Verbs that can be used in an intransitive or transitive way are called ambitransitive verbs. In English, an example is the verb to eat; the sentences You eat (with an intransitive form) and You eat apples (a transitive form that has apples as the object) are both grammatical.
Transitivity is a linguistics property that relates to whether a verb, participle, or gerund denotes a transitive object. It is closely related to valency , which considers other arguments in addition to transitive objects.
For example, If P, then Q. P. ∴ Q. In this example, the first premise is a conditional statement in which "P" is the antecedent and "Q" is the consequent. The second premise "affirms" the antecedent. The conclusion, that the consequent must be true, is deductively valid.
Transitivity (grammar), a property regarding whether a lexical item denotes a transitive object; Transitive verb, a verb which takes an object; Transitive case, a grammatical case to mark arguments of a transitive verb
For example, that every equivalence relation is symmetric, but not necessarily antisymmetric, is indicated by in the "Symmetric" column and in the "Antisymmetric" column, respectively. All definitions tacitly require the homogeneous relation R {\displaystyle R} be transitive : for all a , b , c , {\displaystyle a,b,c,} if a R b {\displaystyle ...
For example, the position and the linear momentum in the -direction of a particle are represented by the operators and , respectively (where is the reduced Planck constant). This is the same example except for the constant − i ℏ {\displaystyle -i\hbar } , so again the operators do not commute and the physical meaning is that the position ...
The classic example is a person indifferent between 7 and 8 grams of sugar and indifferent between 8 and 9 grams of sugar, but who prefers 9 grams of sugar to 7. [1] Similarly, the Sorites paradox can be resolved by weakening assumed transitivity of certain relations to quasitransitivity.