Answer these- some are True or false Questions.
1a. Is there a transfinite number between that of a Denumerable Set and the numbers of the Continuum ?
1b. Can the Continuum of numbers be considered a Well-Ordered Set?
2. Can the axioms of logic be proven to be consistent?
3. Are there two tetrahedra which cannot be decomposed into congruent tetrahedra directly or by adjoining congruent tetrahedra.
4. If the ordering and incidence axioms are retained, the congruence axioms weakened, and the equivalent of the Parallel Postulate omitted, finds whose axioms are closest to those of Euclidean Geometry.
5. Can the assumption of differentability for functions defining a continuous transformation group be avoided?
6. Can physics be axiomized?
7. Is transcendental if 0, 1 is Algebraic and is irrational?
8. Prove the Riemann Hypothesis.
9. Construct generalizations of the Reciprocity Theorem of Number Theory.
10. Is there a universal algorithm for solving Diophantine Equations?
2007-07-03
07:03:16
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3 answers
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asked by
a2z_alterego
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Science & Mathematics
➔ Mathematics
11. Extend the results obtained for quadratic fields to arbitrary integer algebraic fields.
12. By explicitly constructing Hilbert class fields using special values, extend a thereom of Kronecker to arbitrary algebraic fields.
13. Show the that solving the general seventh degree equation by functions of two variables is an impossibility.
14. Show the finiteness of systems of relatively integral functions.
15. Justify Schubert's Enumerative Geometry.
16. Develop a topology of real algebraic curves and surfaces.
17. Find a representation of definite form by squares.
18. With congruent polyhedra, build spaces.
19. Analyze the analytic character of solutions to variational problems.
20. Solve general Boundary Value Problems.
21. Prove that there always exists a Fuchsian System with given singularities and a given Monodromy Group.
22. Uniformization.
23. Extend the methods of Calculus of Variations.
2007-07-03
07:03:43 ·
update #1
sorry some special charactors did not show up. Ignore those questions.
2007-07-03
07:09:04 ·
update #2