The aim of this paper is to demonstrate that several non–rigorous methods of mathematical reasoning in the field of divergent series, mostly related to the Euler and Hutton transforms , may be developed in a correct and consistent way by methods of the grossone analysis.
One of the main aims of phylogenomics is the reconstruction of objects defined in the leaves along the whole phylogenetic tree to minimize the specified functional, which may also include the phylogenetic tree generation. Such objects can include nucleotide and amino acid sequences, chromosomal structures, etc. The structures can have any set of linear and… (More)
MSC (2010) 03E15 We prove several dichotomy theorems which extend some known results on σ-bounded and σ-compact-pointsets. In particular we show that, given a finite number of Δ 1 1 equivalence relations F1 ,. .. , Fn , any Σ 1 1 set A of the Baire space either is covered by compact Δ 1 1 sets and lightface Δ 1 1 equivalence classes of the relations Fi , or… (More)
In the early years of set theory, Du Bois Reymond introduced a vague notion of infinitary pantachie meant to symbolize an infinity bigger than the infinity of real numbers. Hausdorff reformulated this concept rigorously as a maximal chain (a linearly ordered subset) in a partially ordered set of certain type, for instance, the set N N under eventual… (More)