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 ‘whole number’ doesn’t include negative integers, with “whole numbers’ starting from 0. On the other hand, professional mathematicians tend to use ‘whole numbers’ to mean ‘numbers without a decimal or fractional part’:
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 “entier” and “ganze Zahl” are used in French ans German.
However, having seen the potential ambiguity of the term (as much as ‘positive whole numbers’ is used in one example on Lexico, as if a clarification were needed, ‘whole numbers’ and ‘negative whole numbers’ are used side by side in another, showing that to some, the usual sense of ‘whole number’ includes positivity), and given my vague childhood memories of learning the term ‘whole numbers’ before I had really been introduced to negative numbers, I understand @Period_Blood’s 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, 整数 probably is the more accurate translation because the same ambiguity exists in both Japanese and Chinese. 整数 can mean both ‘positive whole number greater than or equal to zero’ and ‘integer’.
That feels weird, considering I am part of the academic sphere (assistant professor at a Japanese University). Also, while I technically switched to “applied mathematics” 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:
We’re going to have a problem here, as I disagree. For me, entier without any further specification would usually mean “un entier naturel” (i.e. from ℕ). I would specify “entier relatif” (or simply say “un relatif” but that might be language abuse) for ℤ. (NB: I haven’t done maths in French in more than 15+ years, so this might all be misremembering on my part).
With all that being said, that’s why people should use symbols with strict definitions, such as ℤ rather than relying on something as fuzzy as natural language
In prépa, I think I usually hear “entier” being used for “entier relatif” if no other clarification is offered. “Entier naturel” typically needs to be specified, since we usually tackle the general case as much as possible. In any case, the “partie entière” is defined using ℤ, and is never called the “partie entière relative”. However, yes, it’s better to use a symbol with a clear definition where possible. (The problem: outside of France, 0 isn’t always an element of ℕ, so even these symbols aren’t perfect.)
Anyway, as specified above, apparently 整数 is ambiguous too, so it seems like ‘whole numbers’ is as good a translation as we can get without further context.
Fun fact: In maths I am used to ℕ meaning “without 0” in mathematics while in CS it’s always “with 0”. I mean, I understand: The CS peeps wouldn’t be able to count anything otherwise But why mathematicians think that 0 is not natural is beyond me.
Interestingly, if somebody says “integer” then I don’t consider this to be a normal word but rather a technical term (as I’m German), so when I hear “integer” I always think “limited subset of numbers from ℤ”, e.g. “64-bit integer”
When it comes to reading, to my great amazement I discovered that I’m currently in a streak of maths-related fiction books
The first one was 博士の愛した数式 where one of the protags is a retired maths professor, and there is quite some maths talk in there; then 容疑者Xの献身 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 I’m 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 すべてがFになる 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 マンガでわかる series. I haven’t read any of them myself but the reviews for the English titles on amazon seem decent from what I’ve seen.
We never know what our professors mean with ℕ, they probably just decide depending on whether it’s easier to prove something with 0 or not
Btw I’m 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 I’m probably biased by CS lingo!
Thanks for starting the better organized tread tls! This is for sure my interest.
As for level, what @Jonapedia has posted first (AをBと置く – let A be B, n乗 – nth power, etc…) 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, I’m pretty sure I can’t 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 人工知能 and 機械学習
CS - Specific CS topics, such as Networks, security, etc… or work-related project discussions.
That’s it. But I’m also not sure on the steps forward so for now, will keep a look on the thread for next steps
I’ve read them in English and super liked them! I’d totally choose this book for a first trial in the reading group. It’s quite lighthearted and I think it really does try to explain complicated topics in a simple and funny way
I updated the wiki post with the vocabulary I posted the other day. There’s actually more that can be extracted from the solution I posted, including terms like ‘relatively prime’, but I should be getting on with other maths (in French) at the moment, so I won’t be doing it myself. I’d encourage everyone else to take a look, especially because the maths involved in the solution shouldn’t be too hard to understand as long as you’ve studied maths up to about high school level.
That’s 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 ℕ 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 didn’t. Depending on what their defaut was they sometimes used notations like ℕ_0 or ℕ\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, that’s 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 isn’t completely thought through but more a “work in progress”.
Thank to everyone taking their time to make sense out of it and already adding some vocabulary terms. I’ll 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. That’s really great. Especially with the web articles we can basically start immediately.
As I don’t 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 I’ve 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. …And I hope it is fine we copy them
One of things I’ve seen in other book clubs is that they create dedicated sub threads for the actual reading. That’s something I’d 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 theorem…) 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 don’t 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
I like the idea of starting with a web resource. I gotta say, I’m 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.
I’m talking about the Microsoft IME. So you type しゅうごう 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
I’ve 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 doesn’t
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 I’d 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 I’ll create a math reading thread (after I’ve done my reviews ) → 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 series… 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.
Because “God made the integers natural numbers; all the rest is the work of Man” to count existing objects. If there is no object, you do not count it. Hence N = {1, 2, …}, while Z = {…, -1, 0, 1,…} Indeed much better to stick to symbols than words for math definitions.
We come into this world with nothing, and we leave this world taking nothing with us, so… isn’t that the most natural state of them all?
But maybe it’s only about assigning a number to this state or not. That’s a stance I can agree on. Thanks!
That being said, I learned all those maths in French, so I might be fuzzy on the English part. Still:
But why mathematicians think that 0 is not natural is beyond me.
) → 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 
