Talk:Arithmetic

Numeralization

Don't you think "numeralization of the null concept" should be changed to "invention of zero"? If not, I think at least "numeralization of the null concept (invention of zero)" should be written instead. This would be much clearer. A.Z.

Arithmetic operations

In modern English, I do not think that the term "arithmetic operations" includes things like logarithmic functions and trigonometric functions. Ebony Jackson (talk) 19:14, 7 February 2021 (UTC)

Number theory a "top-level area" of math?

User:D.Lazard I don't see how my edit broke the logical structure of the phrase. And I disagree that number theory is a "top-level" area of modern math. According to Mathematics Subject Classification number theory is not a first-level branch of math. --L'âne onyme (talk) 17:52, 27 October 2021 (UTC)

Yes it is, it is number 11 under MSC's level 1. MrOllie (talk) 18:09, 27 October 2021 (UTC)

You are right, I didn't see that. However that doesn't make number theory a "broad area" or more important than other branches like say MSC 31 "Potential theory". --L'âne onyme (talk) 18:23, 27 October 2021 (UTC)

If the study of integers isn't a broad or important area, I'm not sure what would be. MrOllie (talk) 18:38, 27 October 2021 (UTC)

That's your point of view. Mine is that number theory is not really a top-level area of math in its own right but rather a mixture of applied algebra and applied analysis. We can only use external sources to settle the debate.

I noticed that in the German article Teilgebiete der Mathematik, which itself refers to Bourbaki's Elements, the division is made between logic/set theory, algebra, analysis and topology. Number theory doesn't appear here. --L'âne onyme (talk) 18:45, 27 October 2021 (UTC)

I prefer Gauss, who said "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." - MrOllie (talk) 19:02, 27 October 2021 (UTC)

Snobbery about number theory not being real mathematics? Really, or is this just trolling? I thought the area to be snobby about was combinatorics. —David Eppstein (talk) 19:06, 27 October 2021 (UTC)

In my school days it was the statisticians who never got invited to parties. MrOllie (talk) 19:08, 27 October 2021 (UTC)

Lol. The question was not about number theory not being real math but whether it is a top-level area of math or not. L'âne onyme (talk) 19:16, 27 October 2021 (UTC)

I would give more weight to the classification that seems to have been made by the members of Bourbaki than to this off-topic quotation from Gauss (who by the way is talking about "arithmetic" and not number theory, a term of rather recent invention). The fact that "number theory" is the "queen of math" does not mean that it is one of the main subdivisions of math. L'âne onyme (talk) 19:32, 27 October 2021 (UTC)

As our article explains, at the time Gauss said that, they were synonyms. MrOllie (talk) 20:24, 27 October 2021 (UTC)

Can we skip to either the part where you flame out and then turn out to be a sock-puppet or the part where you knock it off, recognize that Wikipedia is not a place to promote your most unconventional attitudes, and become a useful contributor, without going through a dozen tedious talk-page WP:NOTFORUM discussions? --JBL (talk) 20:33, 27 October 2021 (UTC)

JBL, I would ask you to assume good faith and be somewhat more polite (in compliance with Wikipedia rules) and tell me when I have been "unconventional" or violated WP:NOTFORUM (an accusation that seems maybe a bit more relevant to the two contributors above) ? I have not taken part in any editing wars and all my arguments are based on sources, not personal views. L'âne onyme (talk) 21:02, 27 October 2021 (UTC)

About alleged Bourbaki's classification (for the record): L'âne onyme refers to de:Teilgebiete der Mathematik, which refers to Bourbaki's Éléments de mathématique without further precision. This German article cannot be considered as a reliable source, because it is unsourced and WP:Wikipedia is not a reliable source. Moreover, the alleged Bourbaki's classification is extracted from the name of the parts of Bourbaki's treatise, without considering that this treatise has never been finished and that some important parts of mathematics have never been included in it. In summary, there is no Bourbaki's classification of mathematics areas. D.Lazard (talk) 16:33, 28 October 2021 (UTC)

operations section covers 4 of 6

The intro paragraph lists: addition, subtraction, multiplication, division, exponentiation, and extraction of roots. Then the section on Arithmetic operations, gives a brief overview of the first four (explaining how they are inverses, etc.), but then the section stops and doesn't finish with the pair of exponentiation, and roots. I think completing the summary would be fitting for this overview article (at the same brief level) without readers having to go to a more specialized article. DKEdwards (talk) 18:55, 23 January 2022 (UTC)

Peano formalizing Arithmetic

The claim that "Peano formalized arithmetic with his Peano axioms," seems misleading given that Peano was building off Dedekind's axiomization. Ted BJ (talk) 01:56, 16 August 2022 (UTC)

I cannnot understand how a man (Peano) can be built off an axiomatization. Moreover, The only Dedekind's axiomization that I know of is Dedekind's construction of real numbers, which cannot be confused with Peano's axiomatization of natural numbers. So, there is nothing misleading here, and I'll remove the tag {{disputed inline}}. D.Lazard (talk) 12:33, 16 August 2022 (UTC)

First of all, by "Peano was building off Dedekind's axiomization" I meant that Peano built his axiomatization off Dedekind's axiomization. This is a very common idiom, for example see here: https://www.google.com/books/edition/Protest_on_the_Page/0JMvBwAAQBAJ?hl=en&gbpv=1&dq=%22was+building+off+earlier%22&pg=PA106&printsec=frontcover

Secondly, Dedekind provided an axiomatization of arithmetic in his 1888 paper "Was sind und was sollen die Zahlen?" aka "What are numbers and what should they be?". See here https://mathcs.clarku.edu/~djoyce/numbers/dedekind.pdf and here http://aleph0.clarku.edu/~djoyce/numbers/peano.pdf. This axiomatization was the basis of for Peano's later axiomatization, so claiming that "Peano formalized arithmetic with his Peano axioms" is misleading, because it leaves out Dedekind's contributions. I will put the tag back. Ted BJ (talk) 15:06, 22 August 2022 (UTC)