Rigorous proof in mathematics is often derived from deductive and inductive reasoning. Deductive reasoning is the premise to achieve complete certainty: it is defined as "reasoning from general to particular" (Lagemaat 121). ... Through rigorous proof, this premises would then follow deductive reasoning: since any number is real, then it is either rational, irrational, an integer, whole, or a natural number. ... Therefore, despite proofs used through reasoning, inductive reasoning does not always maintain complete certainty. ... However, Fermat had to surpass inductive and deductive ...

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Incorrectness of reasoning or belief; erroneousness. 4. ... Sometimes called circular reasoning, vicious circularity, and vicious circle fallacy. ... A person needs to be able to identify major forms of inductive reasoning and apply methods for evaluating them. ... They also need to be able to identify deductive arguments and apply methods for evaluating their validity and invalidity. ...

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• Grade Level: High School