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Unlike with functions, notational ambiguities can be overcome by means of additional definitions (e.g., rules of precedence, associativity of the operator). For example, in the programming language C , the operator - for subtraction is left-to-right-associative , which means that a-b-c is defined as (a-b)-c , and the operator = for assignment ...
The English modal auxiliary verbs are a subset of the English auxiliary verbs used mostly to express modality, properties such as possibility and obligation. [a] They can most easily be distinguished from other verbs by their defectiveness (they do not have participles or plain forms [b]) and by their lack of the ending ‑(e)s for the third-person singular.
That can indeed hinder. You can, if you are allowed. She can really sing. could: That could happen soon. – He could swim when he was young. may: That may be a problem. May I stay? – might: The weather might improve. Might I help you? – must: It must be hot outside. Sam must go to school. – shall: This shall not be viewed kindly. You ...
While the first interpretation may be expected by some users due to the nature of implied multiplication, [38] the latter is more in line with the rule that multiplication and division are of equal precedence. [3] When the user is unsure how a calculator will interpret an expression, parentheses can be used to remove the ambiguity. [3]
This can also apply to limits: see Vanish at infinity. weak, weaker The converse of strong. well-defined Accurately and precisely described or specified. For example, sometimes a definition relies on a choice of some object; the result of the definition must then be independent of this choice.
The converse may or may not be true, and even if true, the proof may be difficult. For example, the four-vertex theorem was proved in 1912, but its converse was proved only in 1997. [3] In practice, when determining the converse of a mathematical theorem, aspects of the antecedent may be taken as establishing context.
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.
The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation. The rules can be expressed in English as: not (A or B) = (not A) and (not B) not (A and B) = (not A) or (not B) where "A or B" is an "inclusive or" meaning at least one of A or B rather than an "exclusive or" that means exactly one of A or B.