Articles
Abstract
V Comprehensive meaning of ∞ and elimination of contradictions
Nov. 2022. The symbol ∞ can only be completely understood if a standard length is assumed. The axiom of infinity defines ∞ by the potentially infinite sequence of standard units of length on the axis of Euclidean space. When non-standard quantities are considered, counts are greater or less than ∞. This also applies to natural numbers resulting from mapping line segments. Cantor premised a single transfinite set of natural numbers, in fact many unlimited infinite sequences of these numbers exist. In contrast to previous theory, consistent calculation rules apply, e.g. ∞ + n > ∞ and ∞ + ∞ = 2 ∞.