Mephist

If I had a reasonable explanation of what the collapse of the wave function means I would immediately publish it and I would become the most famous ph...

But the wave functions in quantum mechanics are not supposed to have the size of the particle that they represent. For example, electrons are supposed...

I think the main point of V.I. Arnold in this article is that the way mathematics is discovered (or invented), is not the way it is taught: when a the...

Do you have a reference to a document where this result (1+2+3+4......... = -1/12) is actually used to calculate the the Casmir Force ? The normal exp...

OK. So you are arguing that space is made of indivisible pieces, and every piece of space is made of a finite quantity of indivisible pieces. I think ...

But to be "discrete" does not mean to be "finite" (https://en.wikipedia.org/wiki/Discrete). Discrete means that is made of parts that are distinct fro...

If you want to show that continuum space implies a contradiction, you should start by assuming as hypothesis that "space is continuum AND one of the t...

I totally agree that the use of logic in mathematical proofs, and the successive refinement of logic to formal logic at the beginning of 20th century,...

Yes, I know Hilbert's program, from the beginning on 20th century (https://plato.stanford.edu/entries/hilbert-program/): all mathematics should be ref...

Here's a video that may interest you: https://www.youtube.com/watch?v=oBOZ2WroiVY Goodstein's theorem is a theorem about a computable function that ca...

Yes, no doubt it's impossible. But nobody says that only computable functions exist.

I see that there is a lot of misunderstanding about constructivism meaning the rejection of actual infinity. Constructivism is not about the rejection...

I think we could interpret natural numbers as properties, or attributes, of physical objects: "5" is an attribute of a physical object that is made of...

Hi @fishfry! OK! as you wish :smile: No problem! Actually, I find Coq is much easier then the paper that you found! But everything depends on your bac...

The definition of real numbers in the Italian paper is on the third page. The last axiom of that definition is this one: completeness: \forall f: N \t...

Let me rephrase the question: "If a sequence is Cauchy in ZFC, is it Cauchy in intuitionist math?" This question is too vague to have an yes/no answer...

Answer: because Cauchy completeness is assumed as an axiom of the theory (this is not a model of the reals because real numbers are described axiomati...

The Italian paper is about a formalization of real numbers in Coq: "We have formalized and used our axioms inside the Logical Framework Coq" (from the...

OK. I see what I am doing wrong: I am making very long premises to be able to refer to them in the following argumentation. But if you start reading t...

x = {-b \pm \sqrt{b^2-4ac} \over 2a} It works!!! :starstruck: :starstruck: :starstruck:

What do you mean by "the standard (ZF) reals"? Maybe I am saying obvious things, but at risk of being pedantic, I prefer to make everything clear abou...

In ZFC a Cauchy succession is a definition, and completeness is a theorem, not an axiom. P.S. OK, sorry. They have Dedekind as an axiom, that is equiv...

OK, I'll rephrase it: if you remove the completeness axiom (consider the same exact theory without that axiom), Cauchy completeness is not provable no...

By the way, just a quick note: as you said they have a completeness AXIOM. Not a completeness theorem. It means that completeness is not provable nor ...

Hi @fishfry! Sorry, but you have to give me some time to learn about how to write symbols on this site, and I have not much time for this right now. O...

Hi! here's what I mean: imagine you don't know anything about geometry: you are a computer without any way to "view" the world: no cameras, computer v...

Yes, that's very interesting. Thank you for the reference! P.S. After reading this, please read my explanation on what is "wrong" with Banach-Tarski p...

Here is a good explanation of what "contructive mathematic" means: https://www.iep.utm.edu/con-math/

That seems to be the common point of all your arguments about real numbers, so I wanted you to show you this: https://mathoverflow.net/questions/12856...

Yes. Consistency and truth are not the same thing. That is one of the main consequences of Godel's incompleteness theorems https://en.wikipedia.org/wi...

In 1940 Godel proved (https://www.sciencedirect.com/science/article/pii/S0049237X08715003) that the "generalized continuum hypothesis" can be added to...

But you have to admit that there must be a way to make sense of the idealized things, because mathematics is essential in nearly all contemporary scie...

Yeah... I see what you mean. But this is not the way how mathematics works. You see, you cannot say that a plane does not exist because it has no widt...

I don't know how to answer to this: division by zero is not defined, OK. But how do you think you can use a value that is not defined? Not defined mea...

OK, let alone BT. In my opinion there are no interesting results that depend in an explicit way on the fact that a continuum line is defined as an unc...

Formal logic (currently assumed as the foundation of mathematics) is only dependent on one very fundamental fact of physics (that usually is not regar...

Can you show me a physical theory, or a result of a physical theory, that is somehow derived from the fact that a continuous line is made of an uncoun...

What's wrong with the Banach-Tarsky paradox ( meaning: how is it possible that you can change the volume of an object by applying only isometric tranf...

It's much less mysterious that you think. First of all, let's use the definition of real numbers as Cauchy sequences. The definition of the Omega numb...

Yes, I really wasn't interested in speaking about Banach-Tarski. I took it only as an example, maybe the wrong one. But on the other hand I am convinc...

What about these dimensions? 1. "Level of individual participation in taking decisions" One side of the dimension: low participation, less control of ...

In physics infinite is a simplification of the measure of an object, when the real measure is big enough to be ignored. So, for example, the electroma...

HOTT is not a constructivist theory (with my definition of constructivism) because it uses a non computable axiom: the univalence axiom (https://ncatl...

Yes, and this clarifies a lot o things about infinity: "In first-order logic, only theories with a finite model can be categorical." (form https://en....

I tried to google for "constructive real numbers are not complete", or something similar. I found this, for example: https://users.dimi.uniud.it/~piet...

First of all, the point about formal systems. I completely agree that the formal proof is not the essential part of a theorem about geometry! I'll tel...

OK, I read the article and finally understood the point about isometry group! :smile: Actually, I tried to look for a formal proof of Banach-Tarski in...

Yes, and that's the point: you can't see the reason why Pythagoras theorem is interesting if you don't look at physical space. Then, we can say Pythag...

Let me give you some simple examples of theorems taken from here: http://www.cs.ru.nl/~freek/100/ to illustrate my idea of "probability measure" for a...

Evidently he thinks that Iran will not respond to an attack starting a war. Otherwise it doesn't make much difference how many people you kill with th...