ButâŠ they are not though. At least not in the definition I learned.

OK, so, I took a look at the Wikipedia page posted by @tls and also at a Quora answer, and apparently the American textbook definition of âwhole numberâ doesnât include negative integers, with âwhole numbersâ starting from 0. On the other hand, professional mathematicians tend to use âwhole numbersâ to mean ânumbers without a decimal or fractional partâ:

https://www.quora.com/Can-negative-numbers-still-be-whole-numbers

This Wikipedia disambiguation page shows that both meanings exist:

Finally, the Oxford and Cambridge dictionaries use the words interchangeably in their definitions:

As such, I think the literal meaning of the word and the academic sphere are solidly on my side. Such usage also matches the way âentierâ and âganze Zahlâ are used in French ans German.

However, having seen the potential ambiguity of the term (as much as âpositive whole numbersâ is used in one example on Lexico, as if a clarification were needed, âwhole numbersâ and ânegative whole numbersâ are used side by side in another, showing that to some, the usual sense of âwhole numberâ includes positivity), and given my vague childhood memories of learning the term âwhole numbersâ before I had really been introduced to negative numbers, I understand @Period_Bloodâs concern and will as such edit my original post to remove such ambiguity.

EDIT: after checking the definitions in Chinese and Japanese, it seems that, ironically, æŽæ° probably **is** the more accurate translation because the same ambiguity exists in both Japanese and Chinese. æŽæ° can mean both âpositive whole number greater than or equal to zeroâ and âintegerâ.

That feels weird, considering I am part of the academic sphere (assistant professor at a Japanese University). Also, while I technically switched to âapplied mathematicsâ from the Master level, my background is in maths That being said, I learned all those maths in French, so I might be fuzzy on the English part. Still:

Weâre going to have a problem here, as I disagree. For me, entier without any further specification would usually mean âun entier naturelâ (i.e. from â). I would specify âentier relatifâ (or simply say âun relatifâ but that might be language abuse) for â€. (NB: I havenât done maths in French in more than 15+ years, so this might all be misremembering on my part).

With all that being said, thatâs why people should use symbols with strict definitions, such as â€ rather than relying on something as fuzzy as natural language

I have added a few random words to the table, so now people can read ćžžćŸźćæčçšćŒ (ordinary differential equation)

In prĂ©pa, I think I usually hear âentierâ being used for âentier relatifâ if no other clarification is offered. âEntier naturelâ typically needs to be specified, since we usually tackle the general case as much as possible. In any case, the âpartie entiĂšreâ is defined using â€, and is never called the âpartie entiĂšre relativeâ. However, yes, itâs better to use a symbol with a clear definition where possible. (The problem: outside of France, 0 isnât always an element of â, so even these symbols arenât perfect.)

Anyway, as specified above, apparently æŽæ° is ambiguous too, so it seems like âwhole numbersâ is as good a translation as we can get without further context.

Whut.

Fun fact: In maths I am used to â meaning âwithout 0â in mathematics while in CS itâs always âwith 0â. I mean, I understand: The CS peeps wouldnât be able to count anything otherwise But why mathematicians think that 0 is not natural is beyond me.

Interestingly, if somebody says âintegerâ then I donât consider this to be a normal word but rather a technical term (as Iâm German), so when I hear âintegerâ I always think âlimited subset of numbers from â€â, e.g. â64-bit integerâ

When it comes to reading, to my great amazement I discovered that Iâm currently in a streak of maths-related fiction books

The first one was ććŁ«ăźæăăæ°ćŒ where one of the protags is a retired maths professor, and there is quite some maths talk in there; then ćźčçè
Xăźçźèș« where one of the protags is a senior high school maths teacher (not that much maths vocab in here but some nice monologues on the beauty and usefulness of mathematics), now Iâm reading 1Q84 where one of the protags is a prep school maths teacher (very little maths vocab so far but a nice monologue on why he likes maths), and ăăčăŠăFă«ăȘă is starting soon (there is apparently a bunch of CS talk in that one). The second and fourth books are written by engineering professors, so I guess that explains a lot

For a more lighthearted/accessible introduction to various topics we could try checking out the ăăłăŹă§ăăă series. I havenât read any of them myself but the reviews for the English titles on amazon seem decent from what Iâve seen.

We never know what our professors mean with â, they probably just decide depending on whether itâs easier to prove something with 0 or not

Btw Iâm also German and I agree with what you said about integers and from our perspective, I also would have thought that whole numbers include the negative ones because the German term would literally be translated as whole numbers

omg I think I solved our divergent opinions! I transitioned to a non-French speaking environment at the same time I transitioned from maths to CS, so Iâm probably biased by CS lingo!

@AWR @tls I will most likely just be stalking the thread. Also, I am just a math hobbyist not at all an expert.

Also AWR I really will spend some time assembling a list of books. I am inundated with things right now, so it will take a few days.

Thanks for starting the better organized tread tls! This is for sure my interest.

As for level, what @Jonapedia has posted first (AăBăšçœźă â let A be B, näč â nth power, etcâŠ) is my level and my interest as well, as I my background is CS and no Japanese technical vocabulary at all.

Random content suggestions, as I have never taken part on book clubs before:

Beginner level:

- Math - Elementary / High School topics, from addition / subtraction to simple equations and their respective explanations.
- CS - Basic computer programming logic, computer architecture (what are the hardware stuff inside the pc and do they do)

After basics, Iâm pretty sure I canât have proper discussions yet but I could think on something like

- Math - College level Calculus/Probability/Stats and applied math. This would be cool because it then joins with interests on äșșć·„ç„èœ and æ©æą°ćŠçż
- CS - Specific CS topics, such as Networks, security, etcâŠ or work-related project discussions.

Thatâs it. But Iâm also not sure on the steps forward so for now, will keep a look on the thread for next steps

Iâve read them in English and super liked them! Iâd totally choose this book for a first trial in the reading group. Itâs quite lighthearted and I think it really does try to explain complicated topics in a simple and funny way

Me too. I also donât have the language skills unless I want to say that I am a complex number:

è€çŽ æ°ă§ă

Maybe I need a thread where Iâll set some maths problems to solve?

There is absolutely no rush.

I updated the wiki post with the vocabulary I posted the other day. Thereâs actually more that can be extracted from the solution I posted, including terms like ârelatively primeâ, but I should be getting on with other maths (in French) at the moment, so I wonât be doing it myself. Iâd encourage everyone else to take a look, especially because the maths involved in the solution shouldnât be too hard to understand as long as youâve studied maths up to about high school level.

Thatâs what my misconception was yesterday. Thanks to both of you for taking the time to clarify it. I really appreciate that.

Thanks for sharing your perspective on â with or without zero. We might run into this while reading different texts and the given sources might handle it differently as well. So it is good thing to keep in mind, I think.

I made similar experience at university. Some professors included the zero and others didnât. Depending on what their defaut was they sometimes used notations like â_0 or â\backslash\{0\} to exceptionally include or exclude the zero.

Also, I like the suggestion @Naphthalene senpai made about adding math notations for clarification from time to time. Thanks for sharing.

Thanks for turning the second post of this thread into a wiki. Yes, thatâs the one

Thanks for sharing feedback and further suggestions on the wiki post.

My main idea yesterday was to provide a basic infrastructure for note taking and discussions. I feel having a wiki post might be helpful as everyone can edit it and we can highlight stuff that becomes important / useful for us along the discussion.

I never mentioned it though, that this isnât completely thought through but more a âwork in progressâ.

Thank to everyone taking their time to make sense out of it and already adding some vocabulary terms. Iâll try to add some clarifications later on or tomorrow but also feel free to make changes in case some ideas come into your mind

Thanks for sharing, this could indeed become in handy. Which IME are you talking about? The one on WK or something else?

I also want to thank everyone sharing different suggestions for web articles or books to read. Thatâs really great. Especially with the web articles we can basically start immediately.

As I donât have much book club experience either I am thinking of lurking a little bit into the different book club formats we already have here in the community. For example Iâve seen some really nice ideas and structuring elememts @Micki senpai is using in the Absolute Beginners Book Club I think will be very helpful for us as well. âŠAnd I hope it is fine we copy them

One of things Iâve seen in other book clubs is that they create dedicated sub threads for the actual reading. Thatâs something Iâd like to apply as well as I feel it keeps the discussion focused. And if others wants to read the same texts at a later time (sef-paced) they have a dedicated entrypoint.

Apart from that, I have a couple of ideas in mind how we could get things started:

- I like @Jonapedia senpais suggestion to look into the
*mondai*they posted yesterday and to extract some vocabulary terms out of it and familiarize ourselves with the phrasing. - This gives us time to collect some further resources on a similar level to read on. It also gives us time to look into some CS based articles we could read. @caiomiyashiro senpai already gave some suggestions topic wise.
- Starting with short articles or only parts of an article (maybe a definition or the phrasing of a theoremâŠ) gives us time to experiment with the format, gauge our level and time we wish to spend on one topic
- We can try to alternate reading math and CS based topics

How do you feel?

Thanks for sharing. We can nominate it for a first book based reading, if you like. We donât have to start with it immediately but it will give everyone that would be interested in reading along time to buy the book.

Thanks for sharing the links to these (upcoming) intermediate and advanced book club readings

Agreed, itâd be nice to keep things organised.

I like the idea of starting with a web resource. I gotta say, Iâm quite excited to get started, so not having to wait several weeks for a book to arrive would be great

We could probably follow the book club method of collecting nominations and then having a poll to decide which resource to tackle. Maybe we could have separate polls for maths and CS? That way we could make sure to keep things balanced.

Iâm talking about the Microsoft IME. So you type ăă ăăă then press space to show the menu of things you can turn that input into, which includes a bunch of logic symbols

Yesterday I kind of hit forum maintenance period but today my changes to the wiki post were saved

Iâve added some guidelines and proposal lists for upcoming readings. I heavily relied on the outline of the other book clubs around and made some adjustments as we might use more web related resources or some durtles might wish to propose papers. Please double check if the changes make any sense to you. Feel free to change and enhance parts of it in case it doesnât

I feel the same. How about scheduling the first book for roughly mid May or beginning of June? So we have time to poll and to order it.

In the meantime we can read short web articles / snippets. To keep the entrance barriers low Iâd suggest to tackle articles / snippets we can go through within one week. Then the commitment needed is very low and we can have a nice mix of different subjects.

Agreed. I made two different subsections for math related suggestions and CS related suggestions. How about having two bi-weekly threads:

- math related articles / snippets
- Cs related articles / snippets

To get things started Iâll create a math reading thread (after Iâve done my reviews ) â we will need some CS related suggestions so we can have a short poll - maybe at the weekend - what to read next week. After this we need more math related suggestions

@NyappyTiramisu and @caiomiyashiro senpai as the *manga de wakaru* series is a seriesâŠ do you feel like recommending a particular book out of the series? This would be a nice tryout if the proposal template works for us as well

Cool. Thanks for clarifying. Definitely sounds helpful.

Edit: and here is the first reading thread

Because âGod made the integers natural numbers; all the rest is the work of Manâ to count existing objects. If there is no object, you do not count it. Hence N = {1, 2, âŠ}, while Z = {âŠ, -1, 0, 1,âŠ} Indeed much better to stick to symbols than words for math definitions.