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  2. Mathematical fallacy - Wikipedia

    en.wikipedia.org/wiki/Mathematical_fallacy

    In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...

  3. Constructive proof - Wikipedia

    en.wikipedia.org/wiki/Constructive_proof

    A constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. A non-constructive proof is a proof that proves the existence of a kind of object without providing an example.

  4. Zero to the power of zero - Wikipedia

    en.wikipedia.org/wiki/Zero_to_the_power_of_zero

    Learn about the mathematical expression 00, which is either defined as 1 or left undefined depending on context. Explore its properties, history, and applications in algebra, analysis, and complex exponents.

  5. Proof sketch for Gödel's first incompleteness theorem

    en.wikipedia.org/wiki/Proof_sketch_for_Gödel's...

    Moreover, one may define a statement form Proof(x,y), which for every two numbers x and y is provable if and only if x is the Gödel number of a proof of the statement S and y = G(S). Proof(x,y) is in fact an arithmetical relation, just as "x + y = 6" is, though a much more complicated one.

  6. Proof by contradiction - Wikipedia

    en.wikipedia.org/wiki/Proof_by_contradiction

    Proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction. The term "assuming the opposite" is also used to describe this method, which is equivalent to the law of excluded middle.

  7. Proofs of Fermat's little theorem - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_Fermat's_little...

    Learn how to prove Fermat's little theorem, which states that for every prime number p and every integer a, a^p ≡ a (mod p). See different methods, such as counting necklaces, using dynamical systems, and applying group theory.

  8. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. Learn about the history, methods, and philosophy of proofs, and see examples of direct, indirect, and contrapositive proofs.

  9. Proof of impossibility - Wikipedia

    en.wikipedia.org/wiki/Proof_of_impossibility

    One of the widely used types of impossibility proof is proof by contradiction.In this type of proof, it is shown that if a proposition, such as a solution to a particular class of equations, is assumed to hold, then via deduction two mutually contradictory things can be shown to hold, such as a number being both even and odd or both negative and positive.

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