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For example, in probability theory, integrals are used to determine the probability of some random variable falling within a certain range. [48] Moreover, the integral under an entire probability density function must equal 1, which provides a test of whether a function with no negative values could be a density function or not.
Two other well-known examples are when integration by parts is applied to a function expressed as a product of 1 and itself. This works if the derivative of the function is known, and the integral of this derivative times is also known. The first example is (). We write this as:
In other words, the whole sentence is not categorized as a noun phrase or a verb phrase, but as a new unit—a sentence—which is an exocentric construction. The rule S → NP VP demonstrates how the combination of these parts creates a new structure that doesn’t directly reflect the properties of its individual components.
An extensional definition gives meaning to a term by specifying its extension, that is, every object that falls under the definition of the term in question.. For example, an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class.
By using the schema one can give an inductive definition for the truth of compound sentences. Atomic sentences are assigned truth values disquotationally.For example, the sentence "'Snow is white' is true" becomes materially equivalent with the sentence "snow is white", i.e. 'snow is white' is true if and only if snow is white.
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Weirdly, many people with long careers kind of expect to be treated badly; they’ve seen plenty of examples of corporate callousness. But Lalgee, 37, said many younger people outside of the ...
For example, in the sentence "As for the little girl, the dog bit her", the subject is "the dog" but the topic is "the little girl". Topic being what is being talked about and the subject being what is doing the action can, also, be distinct concepts from the concept agent (or actor)—the "doer", which is defined by semantics , that is, by the ...