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A contronym is a word with two opposite meanings. For example, the word cleave can mean "to cut apart" or "to bind together". This feature is also called enantiosemy, [1] [2] enantionymy (enantio-means "opposite"), antilogy or autoantonymy. An enantiosemic term is by definition polysemic.
Opposites may be viewed as a special type of incompatibility. [1] Words that are incompatible create the following type of entailment (where X is a given word and Y is a different word incompatible with word X): [2] sentence A is X entails sentence A is not Y [3] An example of an incompatible pair of words is cat : dog:
An antithesis must always contain two ideas within one statement. The ideas may not be structurally opposite, but they serve to be functionally opposite when comparing two ideas for emphasis. [4] According to Aristotle, the use of an antithesis makes the audience better understand the point the speaker is trying to make. Further explained, the ...
Indeed, the above proof that the law of excluded middle implies proof by contradiction can be repurposed to show that a decidable proposition is ¬¬-stable. A typical example of a decidable proposition is a statement that can be checked by direct computation, such as "is prime" or "divides ".
The following example in first-order logic (=) is a sentence. This sentence means that for every y, there is an x such that =. This sentence is true for positive real numbers, false for real numbers, and true for complex numbers. However, the formula
Binary opposition is the system of language and/or thought by which two theoretical opposites are strictly defined and set off against one another. [1] It is the contrast between two mutually exclusive terms, such as on and off, up and down, left and right. [ 2 ]
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 ...
Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. [2] Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That ...