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Mathematical logic is the study of formal logic within mathematics.Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory).
Dividing both sides by 2 yields b 2 = 2c 2. But then, by the same argument as before, 2 divides b 2 , so b must be even. However, if a and b are both even, they have 2 as a common factor.
A false premise is an incorrect proposition that forms the basis of an argument or syllogism. Since the premise (proposition, or assumption) is not correct, ...
A polysyllogism is a complex argument (also known as chain arguments of which there are four kinds: polysyllogisms, sorites, epicheirema, and dilemmas) [1] that strings together any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on.
The Pythagorean theorem has at least 370 known proofs. [1]In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. [a] [2] [3] The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.
[1] [2] The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. [3] In modern logic, an axiom is a premise or starting point for reasoning. [4] In mathematics, an axiom may be a "logical axiom" or a "non ...
The following is an example of a false dilemma with the simple constructive form: (1) "If you tell the truth, you force your friend into a social tragedy; and therefore, are an immoral person". (2) "If you lie, you are an immoral person (since it is immoral to lie)". (3) "Either you tell the truth, or you lie".
[1]: 1–2 Old Irish verbs that have no prefixes , called "simple verbs", have two sets of endings, absolute and conjunct. The conjunct endings are used after a variety of grammatical particles , including among others the negative particle ní ("not"), the interrogative particle in , and prepositions combined with the relative pronoun (e.g ...