Are there counter-examples to strong representability by a merely normalized probability like function? (only closed singletons , unit,0?

William Balthes @William_Balthes

09 September 2017 0 1K Report

It is well known that for a total qualitative probability order 〈 S, F=𝒫 (S), ⪋ 〉↦ S, F=𝒫 (S),P〉

Scotts axiom's, in addition to (1), (2), (3)

tothe axioms of non negativity :

(1)∀ (A_i)∈ F: · {A}≥ ∅

2Non triviality

{S}>∅

3. comparability ∀ (A,B)∈ F: : [B >A]⊻ [A=o B] ]⊻ A=B⇔ PR(A)=P(A)=P(A)

Badges
Science topic

More William Balthes's questions See All

What should be used to instead of '='mean equal in the order, /numerically equal in value for non numerically identical events in order theory?

Suppose one has a numerical order (objective probability) that is to be represented by another numerical order F (subjective probability) .Where the events are ordered pointwise numerically. W...

09 October 2017 3,020 0 View

Is the 2 canonical probability simplex (triples)uniquely represented by a vector probability function ranked point-wise,/numerically by tself ?

Ie where the function is non negative and bounded 0

09 October 2017 7,981 1 View

Difference between an order automorphism and order isomoprhism?

Is there any difference between an order iso-morphism (often defined as a -bi-jective (or sur-jective ) order embedding and an order auto-morph-ism in the context of the same numerical domain of...

09 October 2017 6,153 16 View

Do strong qualitative probabilistic representations over finite sets constitute order isomorphisms when not unique or an order emebdding without =?

When a complete comparative qualitative probability order defined over a finite but complete power algebras that is complete in the order. \forall events in P(\omega): A

09 October 2017 2,206 0 View

Is the Canonical unit 2 standard probability simplex closed under all and only convex combinations of two values and which sum to any value in (0,1)?

Is the canonical unit 2 standard probability simplex, the convex hull of the equilateral triangle in the three dimensional Cartesian plane whose vertices are (1,0,0) , (0,1,0) and (0,0,1) in...

07 August 2017 4,386 2 View

State dependenent additivity and state indenpendent additivity ; akin to the cauchy kolmorgov additivity distinction?

State dependent additivity and state independent additivity? ; akin to more to cauchy additivity versus local kolmorgov additivity/normalization of subjective credence/utility, in a simplex...

07 August 2017 8,614 1 View

Midpoint convex monotone increasing F on closed interval rationally convex? linear with three fixed pts

presume that midpoint convex F: [0,1] to [0,1] is monotone increasing (not necessarily strictly ) F(0)=0 ,F(0.5)=0.5 F(1)=1 , As its monotone increasing and midpoint convex with F(0)=0 F(1)=1 it...

06 July 2017 1,275 0 View

Are these two pieces of notations equivalent

is the notation,'≧' equivalent to ≥ ,likewise,are tfor greater then or equal to, at least in the context of analysis or order theory is notation for super ⫆ equivalent to ⊇ .? I am seen this use...

06 July 2017 4,585 1 View

F:[0,1]to[0,1]Functional equation,ifF(x)+F(y)=1\F(x)+F(y)+F(z)=1,cauchy's equation over the unit triangle with F(1)=1 i

Is the following function F:[0,1] to [0,1] F strictly monotonic increasing F(1)=1,(i presume this unnecessary as its specified by the first two (1)ie x+y=1 if and only iof F(x)+F(y)=1...

05 June 2017 10,098 1 View

Rendering curves parallel, point reflection symmetry versus midpoint convexity of mirror symmetric strictly increasing probabilitty functions

Am i correct in presuming that probability function satisfying point reflection symmetry at all points would be linear, ie F-1(x)=F(x); where F(x) is a bi-jective strictly increasing function...

03 April 2017 3,709 0 View

1. If I can quantize the atom using this hyperbolic spiral and classical physics, could nature do the same?

If we map as a continuous motion an ionising electron (beginning its journey at n=1) in an H atom, a specific hyperbolic spiral appears (see animation). When we solve this spiral formula, we find...

07 August 2024 5,343 2 View

Stability of the Solar System: Insights from Einstein’s Equations ?

The stability of the Solar System is a complex subject that blends the classical framework of Newtonian mechanics with the modern insights provided by General Relativity (GR). Understanding this...

07 August 2024 2,569 1 View

Is it possible to plot the atom-projected band structure using GPAW?

Hi, I'm currently working on a project where I need to plot the atom-projected band structure using GPAW. I've been able to calculate the band structure for my material, but I'm having trouble...

07 August 2024 269 3 View

Gromacs first step of minimization ?

I have face this problem anyone help me how to solve this issue ?which is below Fatal error: There are inconsistent shifts over periodic boundaries in a molecule type consisting of 78 atoms. The...

07 August 2024 2,598 1 View

Should I include H atom into C3N5 when i am doing DFT modelling?

Hi all, my experimental XPS results shown that my C3N5 sample consists of N-H bond, hence in this case I should incorporate the N-H bond into my DFT modelling. However, I do notice several papers...

07 August 2024 8,414 2 View

Are there any good simple systems or platforms to recommend?

In order to show people the beauty of control and enhance enthusiasm for learning control theories, are there any good simple systems or platforms to recommend?

05 August 2024 10,034 1 View

"A Markov-like Model for Patient Progression"?

A Markov-like Model for Patient Progression" Markov Chain Monte Carlo (MCMC) Markov Chain Monte Carlo (MCMC) is a powerful computational technique used to draw samples from a probability...

05 August 2024 10,079 0 View

Why do exism movements become permanent dictatorship threats within liberal democracy thinking under majority rule-independent rule of law system?

Exism movements after gaining power within liberal democracies under majority rule and independent rule of law system become permanent dictatorship threats, but why this is the case is not clear...

04 August 2024 8,125 3 View

How to use Density Functional Theory to calculate carrier mobilities of solid system?

Hello, everyone. I have tried to determine carrier motilities of some materials, by Density Functional Theory, using Quantum ESPRESSO. There are a few methods to do it, like a package called...

04 August 2024 8,894 1 View

The Optimal Experimental Approach for Gene Function Analysis?

What is the most suitable experimental setting to understand the consequences of a particular gene: (1) targeted degradation of the specific transcription factor (TF) of the gene, followed by...

04 August 2024 6,265 1 View