Articles
Abstract
III Cantor's faults in his doctrine of the transfinite
April 2023 Existence of the transfinite is disproved by article II. Hypothetically presuming existence, Cantor's works is scrutinised. The antagonistic disparity of transfinite ordinal and cardinal numbers is rebutted, the continuum hypothesis is demonstrated to be wrong. The ostensible equality of sets of points of extremely different geometrical objects, such as a small segment and n- dimensional space, is falsified. The paradox of equivalent transfinite sets and subsets, seemingly suspending Euclid's 5. axiom, "the whole is greater than the part", is resolved. Euclid's axiom is safeguarded.