Related papers: Convergence on surreals
We prove a curious identity for the Bernoulli numbers.
We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued…
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
In this paper we study some basic properties of rough $I$-convergent double sequences in the line of D$\ddot{u}$ndar [8]. We also study the set of all rough $I$-limits of a double sequence and relation between boundedness and rough…
We obtain a good upper bound on the number of solutions of a diophantine equation arising from a strictly convex sequences of real numbers.
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
If we know that some kind of sequence always converges, we can ask how quickly and how uniformly it converges. Many convergent sequences converge non-uniformly and, relatedly, have no computable rate of convergence. However proof-theoretic…
This is the first in a set of three papers providing an introduction to generalised Cesaro convergence. We start with traditional Cesaro methods for extending classical convergence and further generalise these to allow the calculation of…
Germs of real-valued functions, surreal numbers, and transseries are three ways to enrich the real continuum by infinitesimal and infinite quantities. Each of these comes with naturally interacting notions of ordering and derivative. The…
We present a, hopefully, elementary mathematical treatment of the computational aspects of congruent numbers, such that an amateur could understand the problem and perform their own calculations.
We establish a general method for simultaneously perturbing a convergent sequence of functions in such a way that the sequence of strong minima of the perturbed functions tend to the strong minimum of their limit.
Based on the structure of Fibonacci sequence, we give a new proof for the irrationality exponents of the Fibonacci real numbers. Moreover, we obtain all the irrationality exponents of the real numbers corresponding to the differences of…
In this treatise on the theory of the continuum of the surreal numbers of J.H. Conway, is proved ,that the three different techniques and hierarchies of the continuums of the transfinite real numbers of Glayzal A. (1937) defined through…
We settle the existence of certain "anti-magic" cubes using combinatorial block designs and graph decompositions to align a handful of small examples.
We study the automorphism group of the field of surreal numbers. Our main structure theorem presents a decomposition of this group into a product of five significant factors. Using the representation of surreal numbers as generalized power…
We study how well a real number can be approximated by sums of two or more rational numbers with denominators up to a certain size.
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
We give an extension of Sister Celine's method of proving hypergeometric sum identities that allows it to handle a larger variety of input summands. We then apply this to several problems. Some give new results, and some reprove already…
Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices…