Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0905.0719

Degree of Negation of an Axiom

Florentin Smarandache
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this article we present the two classical negations of Euclid's Fifth Postulate (done by Lobachevski-Bolyai-Gauss, and respectively by Riemann), and in addition of these we propose a partial negation (or a degree of negation) of an axiom in geometry. The most important contribution of this article is the introduction of the degree of negation (or partial negation) of an axiom and, more general, of a scientific or humanistic proposition (theorem, lemma, etc.) in any field - which works somehow like the negation in fuzzy logic (with a degree of truth, and a degree of falsehood), or like in neutrosophic logic [with a degree of truth, a degree of falsehood, and a degree of neutrality (i.e. neither truth nor falsehood, but ambiguous, unknown, indeterminate)].

Explore related subjects

math.GM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Florentin Smarandache. 2010-11-17. Degree of Negation of an Axiom. https://arxiv.org/abs/0905.0719

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Combinatorial Problem in Cinema Seating

We address a problem concerning cinema audiences: ``A cinema has $n$ seats numbered from $1$ to $n$, and there are $n$ people with tickets numbered from $1$ to $n$. People enter the cinema in order. If someone has the ticket number $i$, they can choose seats whose numbers are multiples of $i$. They should exit the cinema if the permitted seats are occupied by previous audience members. In how many ways can they be seated under these conditions?" We give an algorithm to create the list of situations that meet these conditions. We also focus on finding the number of situations in two special cases: when exactly one seat is unoccupied whose total number is denoted by $ω(n)$, and when all audiences $1, \ldots, n-1$ are seated, whose total number is denoted by $ψ(n)$. Giving the recursive formula $ψ(n)=1+\sum_{d|n, d\neq n}ψ(d)$ with the initial value $ψ(1)=1$, we provide an explicit formula for $ψ(p^αq^β)$, where $p$ and $q$ are distinct prime numbers. Furthermore, we show that $ω(n)=-n+\sum_{i=1}^nψ(i)$.

math.GM↗
arXiv2026

Quelques remarques sur les vari{é}t{é}s, fonctions de Green et formule de Stokes

We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces of Sobolev spaces, the distance function, the notion of degree and a duality theorem, the variational formulation and conformal map in dimension 2, the metric on the boundary of a Lipschitz domain and polar geodesic coordinates and the Gauss-Bonnet formula and the positive mass theorem in dimension $ \geq 3 $ and in the flat and non flat case. And the Ricci flow. And fields and their relation to the equations.And obstructions in astronomy. And on strings, superstrings and D-branes. And topological solutions in the negative case, critical, supercritical and superstrings and symmetry. And geometrization. And Decision problem, SAT problem and p=np problem.

math.GM↗
arXiv2026

Counting Truchet Tile Balls

A formula is established that counts the number of different balls that can be made by decorating the pentagons and hexagons of a classic football with Truchet-like patterns.

math.GM↗