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- Proof_of_impossibility abstract "A proof of impossibility, also known as impossibility theorem, negative proof, or negative result, is a proof demonstrating that a particular problem cannot be solved, or cannot be solved in general. Often proofs of impossibility have put to rest decades or centuries of work attempting to find a solution. Proofs of impossibility are usually expressible as universal propositions in logic (see universal quantification).One of the most famous proofs of impossibility was the 1882 proof of Ferdinand von Lindemann showing that the ancient problem of squaring the circle cannot be solved, because the number π is transcendental (non-algebraic) and only a subset of the algebraic numbers can be constructed by compass and straightedge. Two other classical problems--trisecting the general angle and doubling the cube—were also proved impossible in the nineteenth century.A problem arising in the sixteenth century was that of creating a general formula using radicals expressing the solution of any polynomial equation of degree 5 or higher. In the 1820s the Abel-Ruffini theorem showed this to be impossible using concepts such as solvable groups from Galois theory, a new subfield of abstract algebra.Among the most important proofs of impossibility of the 20th century were those related to undecidability, which showed that there are problems that cannot be solved in general by any algorithm at all. The most famous is the halting problem.In computational complexity theory, techniques like relativization (see oracle machine) provide \"weak\" proofs of impossibility excluding certain proof techniques. Other techniques like proofs of completeness for a complexity class provide evidence for the difficulty of problems by showing them to be just as hard to solve as other known problems that have proven intractable.".
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- Proof_of_impossibility wikiPageWikiLink 16th_century.
- Proof_of_impossibility wikiPageWikiLink Abel–Ruffini_theorem.
- Proof_of_impossibility wikiPageWikiLink Abstract_algebra.
- Proof_of_impossibility wikiPageWikiLink Alan_Turing.
- Proof_of_impossibility wikiPageWikiLink Alfred_North_Whitehead.
- Proof_of_impossibility wikiPageWikiLink Algebraic_equation.
- Proof_of_impossibility wikiPageWikiLink Algebraic_number.
- Proof_of_impossibility wikiPageWikiLink Alonzo_Church.
- Proof_of_impossibility wikiPageWikiLink Andrew_Hodges.
- Proof_of_impossibility wikiPageWikiLink Andrew_Wiles.
- Proof_of_impossibility wikiPageWikiLink Angle_trisection.
- Proof_of_impossibility wikiPageWikiLink Antinomy.
- Proof_of_impossibility wikiPageWikiLink Arrows_impossibility_theorem.
- Proof_of_impossibility wikiPageWikiLink Axel_Thue.
- Proof_of_impossibility wikiPageWikiLink Bertrand_Russell.
- Proof_of_impossibility wikiPageWikiLink Cantors_diagonal_argument.
- Proof_of_impossibility wikiPageWikiLink Category:Mathematical_logic.
- Proof_of_impossibility wikiPageWikiLink Category:Mathematical_proofs.
- Proof_of_impossibility wikiPageWikiLink Category:Methods_of_proof.
- Proof_of_impossibility wikiPageWikiLink Category:Possibility.
- Proof_of_impossibility wikiPageWikiLink Compass-and-straightedge_construction.
- Proof_of_impossibility wikiPageWikiLink Completeness_(logic).
- Proof_of_impossibility wikiPageWikiLink Complexity_class.
- Proof_of_impossibility wikiPageWikiLink Computational_complexity_theory.
- Proof_of_impossibility wikiPageWikiLink Conservation_of_energy.
- Proof_of_impossibility wikiPageWikiLink Constructible_number.
- Proof_of_impossibility wikiPageWikiLink Constructible_polygon.
- Proof_of_impossibility wikiPageWikiLink Constructive_proof.
- Proof_of_impossibility wikiPageWikiLink Counterexample.
- Proof_of_impossibility wikiPageWikiLink Cube_root.
- Proof_of_impossibility wikiPageWikiLink David_Hilbert.
- Proof_of_impossibility wikiPageWikiLink Decision_problem.
- Proof_of_impossibility wikiPageWikiLink Diophantine_equation.
- Proof_of_impossibility wikiPageWikiLink Diophantine_set.
- Proof_of_impossibility wikiPageWikiLink Doubling_the_cube.
- Proof_of_impossibility wikiPageWikiLink E._M._Wright.
- Proof_of_impossibility wikiPageWikiLink Economics.
- Proof_of_impossibility wikiPageWikiLink Edward_Beltrami.
- Proof_of_impossibility wikiPageWikiLink Emil_Leon_Post.
- Proof_of_impossibility wikiPageWikiLink Entscheidungsproblem.
- Proof_of_impossibility wikiPageWikiLink Epistemology.
- Proof_of_impossibility wikiPageWikiLink Equilateral_polygon.
- Proof_of_impossibility wikiPageWikiLink Ernest_Nagel.
- Proof_of_impossibility wikiPageWikiLink Eulers_sum_of_powers_conjecture.
- Proof_of_impossibility wikiPageWikiLink Ferdinand_von_Lindemann.
- Proof_of_impossibility wikiPageWikiLink G._H._Hardy.
- Proof_of_impossibility wikiPageWikiLink Galois_theory.
- Proof_of_impossibility wikiPageWikiLink Georg_Cantor.
- Proof_of_impossibility wikiPageWikiLink Gregory_Chaitin.
- Proof_of_impossibility wikiPageWikiLink Greibachs_theorem.
- Proof_of_impossibility wikiPageWikiLink Halting_problem.
- Proof_of_impossibility wikiPageWikiLink Hans_Reichenbach.
- Proof_of_impossibility wikiPageWikiLink Hilberts_tenth_problem.
- Proof_of_impossibility wikiPageWikiLink Holmstrxc3xb6ms_theorem.
- Proof_of_impossibility wikiPageWikiLink Irrational_number.
- Proof_of_impossibility wikiPageWikiLink James_R._Newman.
- Proof_of_impossibility wikiPageWikiLink Kolmogorov_complexity.
- Proof_of_impossibility wikiPageWikiLink Kurt_Gödel.
- Proof_of_impossibility wikiPageWikiLink Liar_paradox.
- Proof_of_impossibility wikiPageWikiLink List_of_unsolved_problems_in_mathematics.
- Proof_of_impossibility wikiPageWikiLink Martin_Davis.
- Proof_of_impossibility wikiPageWikiLink Mathematical_induction.
- Proof_of_impossibility wikiPageWikiLink Mathematical_proof.
- Proof_of_impossibility wikiPageWikiLink Natural_science.
- Proof_of_impossibility wikiPageWikiLink Oracle_machine.
- Proof_of_impossibility wikiPageWikiLink Parallel_postulate.
- Proof_of_impossibility wikiPageWikiLink Penrose_tiling.
- Proof_of_impossibility wikiPageWikiLink Perpetual_motion.
- Proof_of_impossibility wikiPageWikiLink Physics.
- Proof_of_impossibility wikiPageWikiLink Pi.
- Proof_of_impossibility wikiPageWikiLink Pierre_de_Fermat.
- Proof_of_impossibility wikiPageWikiLink Political_science.
- Proof_of_impossibility wikiPageWikiLink Post_correspondence_problem.
- Proof_of_impossibility wikiPageWikiLink Post–Turing_machine.
- Proof_of_impossibility wikiPageWikiLink Prime_factor.
- Proof_of_impossibility wikiPageWikiLink Principia_Mathematica.
- Proof_of_impossibility wikiPageWikiLink Proof_by_contradiction.
- Proof_of_impossibility wikiPageWikiLink Proof_by_infinite_descent.
- Proof_of_impossibility wikiPageWikiLink Pythagoras.
- Proof_of_impossibility wikiPageWikiLink Quantum_mechanics.
- Proof_of_impossibility wikiPageWikiLink Rational_number.
- Proof_of_impossibility wikiPageWikiLink Rices_theorem.
- Proof_of_impossibility wikiPageWikiLink Richards_paradox.
- Proof_of_impossibility wikiPageWikiLink Sheila_Greibach.
- Proof_of_impossibility wikiPageWikiLink Solvable_group.
- Proof_of_impossibility wikiPageWikiLink Special_relativity.
- Proof_of_impossibility wikiPageWikiLink Speed_of_light.
- Proof_of_impossibility wikiPageWikiLink Square_root_of_2.
- Proof_of_impossibility wikiPageWikiLink Squaring_the_circle.
- Proof_of_impossibility wikiPageWikiLink Torkel_Franzén.
- Proof_of_impossibility wikiPageWikiLink Transcendental_number.