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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.
If, for example, the Sun were replaced by a black hole of equal mass, the orbits of the planets would be essentially unaffected. A stellar mass black hole can pull in a substantial inflow of surrounding matter, but only if the star from which it formed was already doing so.
The term antonym (and the related antonymy) is commonly taken to be synonymous with opposite, but antonym also has other more restricted meanings. Graded (or gradable) antonyms are word pairs whose meanings are opposite and which lie on a continuous spectrum (hot, cold).
The word "inflammable" can be derived by two different constructions, both following standard rules of English grammar: appending the suffix -able to the word inflame creates a word meaning "able to be inflamed", while adding the prefix in-to the word flammable creates a word meaning "not flammable".
The first published English grammar was a Pamphlet for Grammar of 1586, written by William Bullokar with the stated goal of demonstrating that English was just as rule-based as Latin. Bullokar's grammar was faithfully modeled on William Lily's Latin grammar, Rudimenta Grammatices (1534), used in English schools at that time, having been ...
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 ...
Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production rules or formation rules). Deductive system, deductive apparatus, or proof system, which has rules of inference that take axioms and infers theorems, both of which are part of the formal ...
Auto-antonym: A word that is encoded with opposing meanings. Absurdity; Excusable negligence: If a behavior is excusable, it is not negligence. Gödel's incompleteness theorems: and Tarski's undefinability theorem; Ignore all rules: To obey this rule, it is necessary to ignore it. Impossible object: A type of optical illusion.