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The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

If Omega_1 and Omega_2 are bounded domains, partialOmega_1, partialOmega_2 are Jordan curves, and phi:Omega_1->Omega_2 is a conformal mapping, then phi (respectively, ...

The locus of the point at which two given circles possess the same circle power is a straight line perpendicular to the line joining the midpoints of the circle and is known ...

Let a graph G have graph vertices with vertex degrees d_1<=...<=d_m. If for every i<n/2 we have either d_i>=i+1 or d_(n-i)>=n-i, then the graph is Hamiltonian.

Inside a ball B in R^3, {rectifiable currents S in BL area S<=c, length partialS<=c} is compact under the flat norm.

Let sigma_1, ..., sigma_4 be four planes in general position through a point P and let P_(ij) be a point on the line sigma_i·sigma_j. Let sigma_(ijk) denote the plane ...

Let (X,B,mu) be a measure space and let E be a measurable set with mu(E)<infty. Let {f_n} be a sequence of measurable functions on E such that each f_n is finite almost ...

Relates evolutes to single paths in the calculus of variations. Proved in the general case by Darboux and Zermelo in 1894 and Kneser in 1898. It states: "When a single ...

Any nondegenerate closed space curve may be nondegenerately deformed into either of the two curves illustrated above. Neither of these can be nondegenerately transformed into ...

Let D be a planar Abelian difference set and t be any divisor of n. Then t is a numerical multiplier of D, where a multiplier is defined as an automorphism alpha of a group G ...