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2. Contraposition - Wikipedia

   en.wikipedia.org/wiki/Contraposition

   Contraposition. In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent inverted and flipped .

3. Proof by contradiction - Wikipedia

   en.wikipedia.org/wiki/Proof_by_contradiction

   More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad impossibile.

4. Cantor's diagonal argument - Wikipedia

   en.wikipedia.org/wiki/Cantor's_diagonal_argument

   A generalized form of the diagonal argument was used by Cantor to prove Cantor's theorem: for every setS, the power setof S—that is, the set of all subsetsof S(here written as P(S))—cannot be in bijection with Sitself. This proof proceeds as follows: Let fbe any functionfrom Sto P(S).

5. Constructive proof - Wikipedia

   en.wikipedia.org/wiki/Constructive_proof

   A constructive proof may also refer to the stronger concept of a proof that is valid in constructive mathematics . Constructivism is a mathematical philosophy that rejects all proof methods that involve the existence of objects that are not explicitly built. This excludes, in particular, the use of the law of the excluded middle, the axiom of ...

6. Proof sketch for Gödel's first incompleteness theorem

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

   For a simplified outline of the proof, see Gödel's incompleteness theorems. The sketch here is broken into three parts. In the first part, each formula of the theory is assigned a number, known as a Gödel number, in a manner that allows the formula to be effectively recovered from the number.

7. Mathematical proof - Wikipedia

   en.wikipedia.org/wiki/Mathematical_proof

   The concept of proof is formalized in the field of mathematical logic. [ 12] A formal proof is written in a formal language instead of natural language. A formal proof is a sequence of formulas in a formal language, starting with an assumption, and with each subsequent formula a logical consequence of the preceding ones.

8. Proof by infinite descent - Wikipedia

   en.wikipedia.org/wiki/Proof_by_infinite_descent

   Proof by infinite descent. In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction [1] used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number ...

9. Artist's proof - Wikipedia

   en.wikipedia.org/wiki/Artist's_proof

   Artist's proof. An artist's proof is an impression of a print taken in the printmaking process to see the current printing state of a plate while the plate (or stone, or woodblock) is being worked on by the artist. [1] A proof may show a clearly incomplete image, often called a working proof or trial impression, but in modern practice is ...