Using some planar geometry, including Pick's theorem on the number of lattice points enclosed within certain polygonal regions, we show that this number is the reciprocal of the golden ratio, whence follows the well-known fact that the golden ratio is irrational....
In this\narticle it is shown that, defining the relative complement of the\nself-referring statement, Cantor's power set theorem cannot be derived.\nMoreover, it is given a refutation of the first proof, the so-called Cantor's\... NB Cocchiarella - 《Journal of Philosophical Logic》 被...
doi:10.1080/00029890.2001.11919771EdsgerTheW.TheDijkstraJayadevTheMisraTheInformaworldThe American Mathematical Monthly
THEOREMBurali-Forti’sPARADOXKant’sOnenessFunctionGeorg Cantor's absolute infinity, the paradoxical class Ω of all ordinals, a non-entity for which being called a "class" is an undeserved dignity, must be the ultimate vexation for mathematical philosophers who hold on to some residual realism ...
Y. Lima and C.G. Moreira, A combinatorial proof of Marstrand's theorem for prod- ucts of regular Cantor sets. Expo. Math. 29 (2011), no. 2, 231-239.Y. Lima and C.G. Moreira, A combinatorial proof of Marstrand's theorem for products of regular Cantor sets, to appear in ...