Talk:Integer

Huh?

In the section "Constuction" the follwing sentence needs fixing: "There exist at least a tenth of such constructions of signed integers" (@Vasywriter:?). Paul August ☎ 01:24, 1 May 2018 (UTC)

Replaced "at least a tenth of" with "at least ten".

--Vasywriter (talk) 11:25, 1 May 2018 (UTC)

Thanks, Paul August ☎ 14:55, 1 May 2018 (UTC)

I'm not so sure that this was the intended meaning. According to Purgy's edit summary, he made a guess as to the number (and this was mangled into the "tenth" statement) and he replaced it by "umpteen". I think, and I don't want to speak for Purgy, that he might have meant something like "zillions" which would also be unacceptable. Perhaps a simple "many" is what is called for. --Bill Cherowitzo (talk) 18:12, 1 May 2018 (UTC)

Well I think that Vasywriter was the one added the that section. Paul August ☎ 19:27, 1 May 2018 (UTC)

Just to reduce guessing about my guess: I guessed the quantity, addressed by "at least a tenth of", to be "at least tens of", and so to be roughly in the interval $[20,199]$ for which in German the term "Zig" (the word ending of the first integer multiples of ten: zwanzig, vierzig, fünfzig, ...) is used. Furthermore, I recall to have seen and heard the use of the word "umpteen" for this purpose, synonymous perhaps to the rare "tens of" and analogous to "thousands of". Please, note that this formulation, in contrast to "at least" or "more than", supplies not only a lower, but also an upper bound in a vague manner (not hundreds). Cheers, Purgy (talk) 06:37, 2 May 2018 (UTC)

Oops. Yes he did, so I guess that "at least ten" is the intended meaning. However, that statement could be considered WP:SYNTH, so maybe "many" should still be considered. --Bill Cherowitzo (talk) 19:55, 1 May 2018 (UTC)

I would suggest being vaguer than "at least ten". "Many" is OK but maybe "a number of" is even better. --Trovatore (talk) 20:48, 1 May 2018 (UTC)

Thanks to all of you for your wise comments. It is encouraging for Wikipedia that clever people take time to carefully examine the meaning of words. Here are some elements:

• 1. "A tenth of" was indeed incorrect; it should have been: "a ten of", but this was too vague. Thanks for pointing out the issue.
• 2. "At least ten" is correct, because the cited paper lists ten different term algebras that can be used to build signed integers.
• 3. The suggestions "umpteem" or "a number of" are also correct and, even more: they are inspiring. Indeed, given any $n>=3$, I think it exists a term algebra having $n$ free constructors, such that there is a bijection between signed integers and the ground terms of this algebra. So, there is an infinity of algebras, which is more than ten.
• 4. However, only those term algebras with a small number of constructors (such as the ten listed in the cited paper) are of practical interest, as the higher the number of constructors, the more complex the proofs (as the number of case disjunctions increases).

So, "more than ten", "many", "an infinity" would all be correct, although they are useful/small algebras and useless/large ones. --Vasywriter (talk) 22:56, 2 May 2018 (UTC)

Subset Dilemma

Can someone explain why the naturals are a subset of the integers given the distinct set theoretic definitions? If an integer is defined by an entire equivalence class of ordered pairs of natural numbers, then the naturals are not themselves a subset of the integers. The article does go on to say that the naturals are embedded in the integers by a mapping n to [(n,0)], but that is just a convoluted way of saying they arent actually the same thing. 50.35.103.217 (talk) 07:28, 1 September 2018 (UTC)

The amount of convolutedness is no hindrance to state something, as long as it is well formed, and I believe that it is not necessary to permanently belabor the difference between "being a subset" and "being embedded", as long as the second is strictly shown once. I consider it a fair use to call the identified objects "the naturals within the integers", abbreviated to "the naturals". Purgy (talk) 07:52, 1 September 2018 (UTC)

Meaning of integers

I think you should tell us what is the meaning of integers 41.116.100.253 (talk) 18:45, 18 January 2022 (UTC)

Meaning of integer

Integer-is colloquially defined as a number that can be written without fractional (component for example ,21,04,0and-2048 are integers 41.116.100.253 (talk) 18:50, 18 January 2022 (UTC)

"Entier relatif" listed at Redirects for discussion

An editor has identified a potential problem with the redirect Entier relatif and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 February 15#Entier relatif until a consensus is reached, and readers of this page are welcome to contribute to the discussion. ~~~~
User:1234qwer1234qwer4 (talk) 20:25, 15 February 2022 (UTC)

Lead section

@D.Lazard reverted my edits as "controversial", which I guess means he disagrees with them. Lazard, what exactly is your problem? The lead has never been discussed before besides the recent comments by 41.116.100.253 that the article does not explain "the meaning of integers", which my edits presumably fix.

Also the comments from Cabillon are not unsourced, they are from the "Earliest Uses of Symbols of Number Theory" page. I guess I also could cite page 114 of https://www.amazon.com/Apprenticeship-Mathematician-Andre-Weil/dp/3764326506 for the part that's the André Weil quote. But Cabillon is listed as a source both on Wikipedia and in published scholarly books like [1]. He was a moderator of the Historia Mathematica mailing list so presumably has at least some authority in this area. . Mathnerd314159 (talk) 21:06, 21 August 2022 (UTC)

Mathematics

What are integers in mathematics 190.80.50.12 (talk) 13:15, 5 October 2022 (UTC)

Read the article. Dhrm77 (talk) 14:52, 5 October 2022 (UTC)

Semi-protected edit request on 10 February 2023

Please change the word "number" to "numbers" (explanation of the german word "Zahlen" which means "numbers" in plural and not "number" in singular) Manloeste (talk) 23:41, 10 February 2023 (UTC)

 Done small jars tc 11:44, 11 February 2023 (UTC)

Limit?

Are there infinitely many integers or is the negative limit -2147483648 and the positive limit 2147483647? 84.151.244.223 (talk) 17:52, 10 August 2023 (UTC)

There are infinitely many integers, as stated in the first paragraph of this article. –jacobolus (t) 17:59, 10 August 2023 (UTC)

Lead sentence

I had a look at the Collins source, I would not consider it too reliable - assuming that the first definition listed must be correct is essentially the tertiary source fallacy. Actually the second sentence is "a member of the set {..., -2, -1, 0, 1, 2, ...}", very close to the current lead (the lead I wrote). The "sum or difference of two natural numbers" and "closure of the natural numbers under subtraction" properties are implied by the current lead's second sentence, about the negative numbers being the additive inverses of the positive numbers. The "rational numbers with denominator 1" property is sort of implied by "a real number that can be written without a fractional component", but maybe it is worth adding to the second paragraph. Regarding "signed number" and "directed number", it seems like they are more associated with the real numbers. Even the Collins source states under the respective definitions that these terms may refer to any number, not just integers. Mathnerd314159 (talk) 05:27, 23 April 2024 (UTC)

The other definition includes the word "integer" when defining "integer". There's no way that this "Science and Technology Encyclopedia" is somehow better than the "Collins Dictionary of Mathematics" on the topic of integers. Thiagovscoelho (talk) 06:02, 29 May 2024 (UTC)

The circularity of defining integer as including negative integers is only apparent. A "negative integer" is defined as "the additive inverse of a natural number", not as an integer that is negative. We could remove the circularity completely by using a different term like "negation of natural number", or a more specific description like "string of minus sign in front of digits", but in practice people call them negative integers.

The Science and Technology Encyclopedia is intended for a broad audience, as opposed to Collins which is aimed at undergraduates but includes material for even advanced scholars. You have not responded to Lazard's point that your definition is too WP:TECHNICAL. Mathnerd314159 (talk) 21:00, 29 May 2024 (UTC)

The term negative integer would intuitively be read as "the subset of integers which are less than 0". This makes the definition of integer unclear without special knowledge. To remedy this, negative integer needs to link to the definition or an article. But there is another problem; This definition is not supported -- either by the cited reference Science and Technology Encyclopedia or Collins Dictionary of Mathematics.

Unless it is somehow incorrect, it would be best to simply use the definition cited and remove the "apparent" circularity.

I can't edit, but I would suggest:

An integer is the number zero (0), a positive natural number whole number (1, 2, 3, etc.) or a negative integer negative whole number (−1, −2, −3, etc.). 24.20.59.206 (talk) 18:25, 27 June 2024 (UTC)

"Whole number" is colloquial. "Natural number" is a better choice. I have edited the lead to hopefully make it simpler, more accurate, and less circular.—Anita5192 (talk) 19:06, 27 June 2024 (UTC)

To me "the negation of a positive natural number" seems a lot more awkward and less concise than "negative integer", but I guess following this train of thought we should define the negative integers in the next sentence, which I have done.

I still think though this whole argument is stupid, the source I cited starts out by stating the integers consist of the positive integers, 0, and the negative integers. This definition is not controversial, and is supported by the sources, however much 24.20.59.206 says otherwise. Mathnerd314159 (talk) 04:05, 28 June 2024 (UTC)

One of my objections to the way the lead was previously worded was that defining the integers as consisting, in part, of the negative integers, when we haven't finished defining the integers, is circular.—Anita5192 (talk) 04:19, 28 June 2024 (UTC)

As I said, the circularity is only apparent. I think repeating "the negation of a positive natural number" is more confusing than using "negative integer" and then defining it. Arguably it was defined as the sequence -1, -2, -3, ... simply by writing "negative integers (-1, -2, -3, ...)". And even so, there is no prohibition in Wikipedia on circular definitions - in fact circular definition mentions that many dictionary-style definitions are circular. Mathnerd314159 (talk) 05:24, 28 June 2024 (UTC)