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Complementary antonyms are word pairs whose meanings are opposite but whose meanings do not lie on a continuous spectrum (push, pull). Relational antonyms are word pairs where opposite makes sense only in the context of the relationship between the two meanings (teacher, pupil). These more restricted meanings may not apply in all scholarly ...
A statement is true up to a condition if the establishment of that condition is the only impediment to the truth of the statement. Also used when working with members of equivalence classes , especially in category theory , where the equivalence relation is (categorical) isomorphism; for example, "The tensor product in a weak monoidal category ...
Since the converse of premise (1) is not valid, all that can be stated of the relationship of P and Q is that in the absence of Q, P does not occur, meaning that Q is the necessary condition for P. The rule of inference for necessary condition is modus tollens: Premise (1): If P, then Q; Premise (2): not Q; Conclusion: Therefore, not P
It is often attached to a technical term to indicate that the exclusive meaning of the term is to be understood. The opposite is non-strict, which is often understood to be the case but can be put explicitly for clarity. In some contexts, the word "proper" can also be used as a mathematical synonym for "strict".
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.
A definition states the meaning of a word using other words. This is sometimes challenging. Common dictionaries contain lexical descriptive definitions, but there are various types of definition – all with different purposes and focuses. A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols).
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. [1] [2] It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
Similar to equation solving, inequation solving means finding what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an inequation or a conjunction of several inequations. These expressions contain one or more unknowns, which are free variables for which values are sought that cause the condition to be fulfilled ...