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The standard of rigor is not absolute and has varied throughout history. A proof can be presented differently depending on the intended audience. To gain acceptance, a proof has to meet communal standards of rigor; an argument considered vague or incomplete may be rejected. The concept of proof is formalized in the field of mathematical logic. [12]
The Standard Model of particle physics is the theory ... proof of the top quark (1995 ... Interactions in the Standard Model. All Feynman diagrams in the model are ...
Proof theory is a major branch [1] ... 1-CA 0 using the method of ordinal diagrams. Provability logic. Provability logic is a modal ...
In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, ...
Standard Model of Particle Physics. The diagram shows the elementary particles of the Standard Model (the Higgs boson , the three generations of quarks and leptons , and the gauge bosons ), including their names, masses, spins, charges, chiralities, and interactions with the strong , weak and electromagnetic forces.
Bertrand's postulate and a proof; Estimation of covariance matrices; Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational
Hilbert's 1927, Based on an earlier 1925 "foundations" lecture (pp. 367–392), presents his 17 axioms—axioms of implication #1-4, axioms about & and V #5-10, axioms of negation #11-12, his logical ε-axiom #13, axioms of equality #14-15, and axioms of number #16-17—along with the other necessary elements of his Formalist "proof theory"—e ...
The notion of analytic proof was introduced into proof theory by Gerhard Gentzen for the sequent calculus; the analytic proofs are those that are cut-free.His natural deduction calculus also supports a notion of analytic proof, as was shown by Dag Prawitz; the definition is slightly more complex—the analytic proofs are the normal forms, which are related to the notion of normal form in term ...