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A typical example is the proof of the proposition "there is no smallest positive rational number": assume there is a smallest positive rational number q and derive a contradiction by observing that q / 2 is even smaller than q and still positive.
Many double-barreled questions can be detected by the existence of the grammatical conjunction "and" in them. [2] [3] This is not a foolproof test, as the word "and" can exist in properly constructed questions. A question asking about three items is known as "trible (triple, treble)-barreled". [4]
However, indirect methods such as proof by contradiction can also be used with contraposition, as, for example, in the proof of the irrationality of the square root of 2. By the definition of a rational number , the statement can be made that " If 2 {\displaystyle {\sqrt {2}}} is rational, then it can be expressed as an irreducible fraction ".
An indirectly self-referential sentence would replace the phrase "this sentence" with an expression that effectively still referred to the sentence, but did not use the pronoun "this." An example will help to explain this. Suppose we define the quine of a phrase to be the quotation of the phrase followed by the phrase itself. So, the quine of:
Since the expression on the left is an integer multiple of 2, the right expression is by definition divisible by 2. That is, a 2 is even, which implies that a must also be even, as seen in the proposition above (in #Proof by contraposition). So we can write a = 2c, where c is also an integer.
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An indirect question is expressed by changing the mood of the main verb from the indicative to the subjunctive. Some rhetoric questions change the verb to the accusative, followed by the infinitive, as if it were a real declarative statement in direct speech [17]). It is normally appropriate to retain the word that introduces the question, but ...
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