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Shall and will. Shall. and. will. Shall and will are two of the English modal verbs. They have various uses, including the expression of propositions about the future, in what is usually referred to as the future tense of English. Historically, prescriptive grammar stated that, when expressing pure futurity (without any additional meaning such ...
A modal verb is a type of verb that contextually indicates a modality such as a likelihood, ability, permission, request, capacity, suggestion, order, obligation, necessity, possibility or advice. Modal verbs generally accompany the base (infinitive) form of another verb having semantic content. [1] In English, the modal verbs commonly used are ...
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.
projection. A projection is, roughly, a map from some space or object to another that omits some information on the object or space. For example, R 2 → R , ( x , y ) ↦ x {\displaystyle \mathbb {R} ^ {2}\to \mathbb {R} , (x,y)\mapsto x} is a projection and its restriction to a graph of a function, say, is also a projection.
Mutatis mutandis is a Medieval Latin phrase meaning "with things changed that should be changed" or "once the necessary changes have been made". [1] [2] [3] It continues to be seen as a foreign-origin phrase (and thus, unnaturalized, meaning not integrated as part of native vocabulary) in English and is therefore usually italicized in writing.
Glossary of mathematical symbols. 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. As formulas are entirely constituted with symbols of various ...
The King's English is less like a dictionary than Modern English Usage: it consists of longer articles on more general topics, such as vocabulary, syntax, and punctuation and draws heavily on examples from many sources throughout. One of its sections is a systematic description of the appropriate uses of shall and will.
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...