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The verbs will and shall, when used as future markers, are largely interchangeable with regard to literal meaning. Generally, however, will is far more common than shall. Use of shall is normally a marked usage, typically indicating formality and/or seriousness and (if not used with a first person subject) expressing a colored meaning as ...
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.
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.
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
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 preceding kinds of definitions, which had prevailed since Aristotle's time, [4] were abandoned in the 19th century as new branches of mathematics were developed, which bore no obvious relation to measurement or the physical world, such as group theory, projective geometry, [3] and non-Euclidean geometry.
The word mathematics comes from Ancient Greek máthēma (μάθημα), meaning "that which is learnt", [7] "what one gets to know", hence also "study" and "science". The word came to have the narrower and more technical meaning of "mathematical study" even in Classical times.