minkwe wrote:gill1109 wrote:Michel, you ignored a crucial sentence. *You* are talking about functions which take values in {-1, +1, “undefined”}.

Wow Richard, you are a mathematician don't make such stupid statements. Next you will tell me the range of tan(x) is

Yes. I will tell you that. It’s very convenient indeed to think of the function “tan” as a mapping from the real line to the union of the real line and a disjoint one-point set {“undefined”}.

The alternative is to define it as a function from the real line with an infinite series of points removed to the real line.

Wikipedia: “Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane from which some isolated points are removed.”

The simple parts of the wikipedia page on trigonometric functions (the parts for school children) uses an old fashioned definition, making it “+infinity” on those points.

minkwe wrote:Joy is 100% right. There is no such thing as a mathematical theorem with loopholes. Richard is wrong, the so-called "loopholes" in Bell's theorem are directly related to oversights in Bell's analysis. In other words, the "loopholes" disprove the theorem. Why else will Richard (and Larsson) try to create a new theorem if the original one was valid? Notwithstanding the fact that Fine first identified the time synchronization flaw in Bell's theorem.

It is not simply a problem with practical application.

Joy is not 100% right. There can be a loophole in an attempt to apply a mathematical theorem to a practical matter.

Larsson and my theorem is a different theorem to the “Bell theorem seen as a math theorem”. The conditions are different, and the conclusion is different.

The theorem of Lasrsson and myself, for instance, applies to the computer simulation “epr-simple”.

Bell’s theorem doesn’t. See

https://arxiv.org/abs/1507.00106[Submitted on 1 Jul 2015 (v1), last revised 10 Apr 2021 (this version, v10)]

Event based simulation of an EPR-B experiment by local hidden variables: epr-simple and epr-clocked

Richard D. Gill

In this note, I analyze the data generated by M. Fodje's (2013, 2014) simulation programs "epr-simple" and "epr-clocked". They were written in Python and published on Github. Inspection of the program descriptions showed that they made use of the detection-loophole and the coincidence-loophole respectively. I evaluate them with appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH (NB: its correctness is conjecture, we do not have proof). The experimental efficiencies turn out to be approximately eta = 81% (close to optimal) and gamma = 55% (far from optimal). The observed values of CHSH are, as they should be, within the appropriately adjusted bounds. Fodjes' detection-loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is close to optimal. The model has the same defect as Pearle's: the joint detection rates exhibit signalling. His coincidence-loophole model is actually a clever modification of his detection-loophole model. Because of this, however, it cannot lead to optimal efficiency.

Comments: This is version 11 of this preprint. Earlier versions incorrectly stated that documentation of Michel Fodje's simulation was inexistent. This version also contains better explanation of my terminology. It is also posted on Researchers.one, article 2020-01-1. Another version on this http URL, preprints202001.0045, is being updated