Continuum Hypothesis
The proposal originally made by Georg Cantor 
that there is no infinite Set with aCardinal Number between that of the ``small'' infinite Set of Integers 
and the``large'' infinite set of Real Numbers 
(the ``Continuum''). Symbolically, the continuumhypothesis is that 
. Gödel showed that no contradiction would arise if the continuumhypothesis were added to conventional Zermelo-Fraenkel Set Theory. However, using a technique called Forcing,Paul Cohen (1963, 1964) proved that no contradiction would arise if the negation of the continuum hypothesis was addedto Set Theory. Together, Gödel's and Cohen's results established that the validity of the continuum hypothesisdepends on the version of Set Theory being used, and is therefore Undecidable (assuming theZermelo-Fraenkel Axioms together with the Axiom of Choice).
Conway and Guy (1996) give a generalized version of the Continuum Hypothesis which is also Undecidable:is 
for every 
?
References
Cohen, P. J. ``The Independence of the Continuum Hypothesis.'' Proc. Nat. Acad. Sci. U. S. A. 50, 1143-1148, 1963. Cohen, P. J. ``The Independence of the Continuum Hypothesis. II.'' Proc. Nat. Acad. Sci. U. S. A. 51, 105-110, 1964. Cohen, P. J. Set Theory and the Continuum Hypothesis. New York: W. A. Benjamin, 1966. Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, p. 282, 1996. Gödel, K. The Consistency of the Continuum-Hypothesis. Princeton, NJ: Princeton University Press, 1940. McGough, N. ``The Continuum Hypothesis.'' http://www.jazzie.com/ii/math/ch/ and http://www.best.com/~ii/math/ch/.
- Jacobi Tensor
- Jacobi Theta Function
- Jacobi Transformation
- Jacobi Triple Product
- Jacobi Zeta Function
- Jacobsthal-Lucas Number
- Jacobsthal-Lucas Polynomial
- Jacobsthal Number
- Jacobsthal Polynomial
- Jaco-Shalen-Johannson Torus Decomposition
- Janko Groups
- Japanese Triangulation Theorem
- Jarnick's Inequality
- j-Conductor
- Jeep Problem
- Jenkins-Traub Method
- Jensen Polynomial
- Jensen's Formula
- Jensen's Inequality
- Jerabek's Hyperbola
- Jerk
- j-Function
- Jinc Function
- j-Invariant
- Jitter