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In a context not requiring rigor, this phrase often appears as a labor-saving device when the technical details of a complete argument would outweigh the conceptual benefits. The author gives a proof in a simple enough case that the computations are reasonable, and then indicates that "in general" the proof is similar. index battle
The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of basis, module, and free module.
In linguistics, a verb phrase (VP) is a syntactic unit composed of a verb and its arguments except the subject of an independent clause or coordinate clause.Thus, in the sentence A fat man quickly put the money into the box, the words quickly put the money into the box constitute a verb phrase; it consists of the verb put and its arguments, but not the subject a fat man.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
[4] [5] automatic differentiation In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation or computational differentiation, [6] [7] is a set of techniques to numerically evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no ...
Adjective phrase (AP), adverb phrase (AdvP), adposition phrase (PP), noun phrase (NP), verb phrase (VP), etc. In terms of phrase structure rules , phrasal categories can occur to the left of the arrow while lexical categories cannot, e.g. NP → D N. Traditionally, a phrasal category should consist of two or more words, although conventions ...
The predicate is a verb phrase that consists of more than one word. In the backyard, the dog barked and howled at the cat. This simple sentence has one independent clause which contains one subject, dog, and one predicate, barked and howled at the cat. This predicate has two verbs, known as a compound predicate: barked and howled. (This should ...
Term rewriting systems can be employed to compute arithmetic operations on natural numbers.To this end, each such number has to be encoded as a term.The simplest encoding is the one used in the Peano axioms, based on the constant 0 (zero) and the successor function S.
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