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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 · 3 answers · asked by a2z_alterego 4 in 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

3 answers

did u try to solve these even once?

please first try to do ur homework urself. u wont learn unless u soil ur hands.

2007-07-03 07:15:07 · answer #1 · answered by Vipin A 3 · 0 1

These are Hilbert's famous 23 problems posed
at the beginning of the 20th century. Why not
look them up on Wikipedia and see what has
been done on them since 1900?
BTW, your statement of problem 7 is not complete.
It should read
Is α^β transcendental if α <> 0 or 1 is algebraic
and β is irrational?
This problem was answered in the affirmative
by Gel'fond in 1929 and independently
by Schneider in 1934.
There is a new book entitled
Making transcendence transparent
by
Burger and Tubbs
which devotes a whole chapter to proving
this theorem.

2007-07-03 14:40:20 · answer #2 · answered by steiner1745 7 · 0 1

just cuz we're good at math doesnt mean we're dum at commen sence. do your own home work and quizes

2007-07-03 14:11:58 · answer #3 · answered by Anonymous · 1 1

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