User talk:D.Lazard

Safe Primes, in RSA

Ok, let's try to discuss here: https://en.wikipedia.org/wiki/Talk:RSA_(cryptosystem)#Safe_Primes,_in_RSA_Key_Generation No "reliable sources" are needed here. Here you just need to think with your own head. This is math. In any case, I do not owe you anything, and I do not demand anything from you.

Coordinate Systems and Analytic Geometry

Moved to Talk:Cartesian coordinate system

 – Nothing personal in this discussion

On "Cardinality"

This is a bit of a dual-purpose post:

(1) I've been thinking about your feedback on Talk:Cardinality from a while back. It seemed strange to me, and I kept wondering why. I know we have our differences in taste, but it seemed strange how different our visions of the article were, and you usually have sensible reasons for making the changes you do. I think I've started to realize the difference, and I was wondering if this made sense to you. I wanted the article to be about the foundational concept of "cardinality", as in, "the emergent phenomena of sets" or "the property that defines 'number'". However, I believe you wanted the article to be about the term as used in "The cardinality of A": the function $A\mapsto |A|$ or "the cardinal number equinumerous to ⁠$A$⁠". Does that sound like a fair assumption to you?

(2) I've noticed the article Cardinality function on $A\mapsto |A|$ doesn't exist. The article should exist, and I think you would do it well. I was wondering if you thought you could convert your version into its own article there? It would also give a more reasonable home to Cardinal arithmetic, which is currently shoehorned into Cardinal number. – Farkle Griffen (talk) 01:38, 5 October 2025 (UTC)

I disagree that Cardinal function should exist: for many definitions of a function, ⁠$A\mapsto |A|$⁠ is not function, since its domain and its codomain should be proper classes. Moreover, without the axiom of choice, its codomain would be a proper class of proper classes. Not sure that you can find a notable book that considers this explicitly.

Cardinal arithmetic is not "shoehorned" into Cardinal number, since cardinal arithmetic describes fundamental properties of cardinal numbers.

Also, Wikipedia articles are normally about concepts, not about terms (see WP:NOTDICT). So, I never wanted to write an article about a term, whichever it is. Moreover, the terms (phrases) you suggest at the end of (1) are not correct. The correct formulation is: cardinal numbers are sets that are defined once for all, such that, for every set ⁠$A$⁠, there is exactly one cardinal number, denoted ⁠$|A|$⁠ that is equinumerous to ⁠$A$⁠.

"Cardinality" is not a foundational concept; it is a subtopic of [[set theory}}. I do know what is "the emergent phenomena of sets"; what I know is that set theory was an emergent theory more 100 years ago. "The property that defines 'number'" is an incorrect formulation, since a property never defines anything. The correct formulation is "numbers are defined for formalizing the property of equinumerosity".

So, our main difference is about the way to present cardinality in Wikipedia. Maybe, I'll discuss this in another post. D.Lazard (talk) 15:39, 6 October 2025 (UTC)

The term "function" is used more broadly than the internal, set-theoretic meaning of a certain subset of a cross product. E.g., all of the uses in Cardinal function are exactly that. Other operations like union $(\cup )$ are also functions of this kind. The concept has plenty of sources backing up its notability. If you don't want to write it, I can go ahead—I just figured I'd let you know since, when I was thinking about how to organize it, it seemed similar to your rewriting of Cardinality. I'm not sure what you mean by "notable book that considers this explicitly." If by "this" you mean, defining $|x|$ without the axiom of choice, Azriel Lévy covers that in this book (pp 15-38).

There are roughly two uses of the term "Cardinality":

"Cardinality", as in, the property which determines whether two sets can be put in 1-1 correspondence or not. The set $\{a,b,c\}$ cannot be put in 1-1 correspondence with $\{a,b,c,d\}$, what determines that is these sets' cardinalities. Note that "number" is not defined here at all, and yet we are still able to consider the concept of cardinality.

"Cardinality" as in, "The cardinality of A" or, a specific object used to represent the concept. A materialization of the concept defined above.

What I mean by "emergent phenomena" is that there is no axiom of ZFC (or other set theory) that gives a criterion of what determines whether or not any two given sets can be put in 1-1 correspondence. The fact that some sets can and some sets can't is a property that arises naturally from the axioms but is not defined by them directly.

I would appreciate it if you finished this conversation here before attempting to move it elsewhere. – Farkle Griffen (talk) 17:25, 6 October 2025 (UTC)

Higher-order derivatives link in derivative article

Hi @D.Lazard, you cited WP:NOTBROKEN as the reason for your revert of my section link change. I made the change because the existing link only goes to the top of the derivative article and not to the Higher-order derivatives section; so the existing wikilink is an incorrect navigation. I'm not one for edit wars, so I won't make a further edit on the article, but you may want to improve the article yourself. Duncnbiscuit (talk) 02:35, 11 October 2025 (UTC)

I do not understand: for me Higher order derivative, higher order derivative, Higher-order derivative, and higher-order derivative link all to Derivative#Higher-order derivatives. Note that if you want the plural, the final "s" must be after "]]". Maybe, the target is not correctly displayed when hovering over a preview. But this does not mean that the published version is incorrect. D.Lazard (talk) 08:36, 11 October 2025 (UTC)

it might be that I mostly access Wikipedia via the Android app, which may well have different behaviour to the Web or IOS versions of Wikipedia. Duncnbiscuit (talk) 08:55, 11 October 2025 (UTC)

This may also depend whether you access to Wikipedia through the application or through the web site with your browser. (reading your post again, this is almost what you said.) D.Lazard (talk) 09:40, 11 October 2025 (UTC)