Talk:Integer

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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)Reply

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User:1234qwer1234qwer4 (talk) 20:25, 15 February 2022 (UTC)Reply

@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)Reply

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

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

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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)Reply

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

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)Reply

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

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)Reply

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)Reply

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)Reply

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)Reply

"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)Reply

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)Reply

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)Reply

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)Reply

"4,738,381,338,321,616,895" is the largest decimarithm (decimal number) who represents the alphanumber "ZZZZZZZZZZZZ". It is the maximum limitic number. I defend the inclusion of the alphanumericities in all the articles of the integer numbers and a creation of the article of the compositarithm (composite number) "4,738,381,338,321,616,895" because it represent the largest dodecadigital passsword (dodecasign) and is composite by nine primarithms (prime numbers), who are "5", "7", "13", "31", "37", "43", "97", "1,297" and "1,678,321".

I defend the inclusion of all the numbers from "0" to "4,738,381,338,321,616,895" and consider them notable, dodecasignally speaking.

200.155.122.131 (talk) 09:08, 19 February 2025 (UTC)Reply

Children need to learn about gigarithms (giant numbers), as the proper number "4,738,381,338,321,616,895", exemplarly, and so on.

2804:18:114A:D92D:C68:5AFF:FECF:E031 (talk) 18:56, 19 February 2025 (UTC)Reply

If you have reliable sources, by all means. But I search for "limitic numbers", "decimarithms", "compositarithm", "primarithms", and "gigarithms" and as far as I can tell, these are all words that you have made up. The number 4,738,381,338,321,616,895 is indeed the number of 12-character passwords (assuming 36 characters), and appears in some places on the web, but none of the sources are what I would consider reliable. Furthermore they only mention the number in passing - there is not enough information to write a substantial article on the number. Mathnerd314159 (talk) 19:29, 19 February 2025 (UTC)Reply

No, I'm sorry, I disagree -- reliable sources are a necessary condition, not a sufficient one. Even if there are reliable sources for this, it does not belong in this article. Obviously that's a statement of my own judgment, but I do happen to be right. It's not even remotely a close call. --Trovatore (talk) 20:04, 19 February 2025 (UTC)Reply

4,738,381,338,321,616,896 permutations form a quantity of dodecadigital alphanumbers (or passwords) between "000000000000" and "ZZZZZZZZZZZZ". "4,738,381,338,321,616,896" is a square number (12th potence of 36 and 24th of 6). Exemplarly, the alphanumber "MENSTRUATION" represents the number "2,949,280,905,937,581,527".

2804:18:147:DC0C:44A0:A8FF:FE69:5F50 (talk) 20:35, 19 February 2025 (UTC)Reply

I see no reason why "dodecadigital alphanumbers", meaning "12-digit numbers in base 36", is any more interesting than "17-digit numbers in base 37", for example. And, no, not all passwords are base-36 numbers, as they can (and are often required to) include lower-case and upper-case letters (so base 62, at minimum) and special characters (from a set that may be site-dependent, so the base is site-dependent), and passwords are not necessarily limited to 12 characters.

As for various Ramanujanisms such as taxicab numbers, if you look hard enough, you can construct a large menagerie of integers with various mathematical properties, but those might belong in a "list of integers with interesting number-theoretic/algebraic/etc. properties" article, at best. Guy Harris (talk) 20:52, 19 February 2025 (UTC)Reply

You have reason. My first commentary is a my mere cult positioning. I am a very passionate citizen by the alphanumericisms and by the 216 Web safe colors (Visibone Anglocentric Color Code). My favorite site Numbermatics contains informations over sedecimarithms (sedecimal numbers) and alphanumbers (base 36).

189.50.186.221 (talk) 21:55, 19 February 2025 (UTC)Reply

That numbermatics site is interesting, I see why you would call for creating Wikipedia pages for each number. But Wikipedia has a policy WP:INDISCRIMINATE - the numbers have to actually be interesting. Basic "facts" like a number's factorization and divisors are not sufficient. Mathnerd314159 (talk) 23:29, 19 February 2025 (UTC)Reply

My positioning: I consider the numbers "4,738,381,338,321,616,895" and "4,738,381,338,321,616,896" notable because the first is composite of nine primarithms ("5", "7", "13", "31", "37", "43", "97", "1,297" and "1,678,321") and represents the giant alphanumber "ZZZZZZZZZZZZ" and the second a giant square (12th potence of 36 and 24th of 6), respectively.

"Four quintillion, seven hundred and thirty-eight quadrillion, three hundred and eighty-one trillion, three hundred and thirty-eight billion, three hundred and twenty-one million, six hundred and sixteen thousand, eight hundred and ninety-five" and "four quintillion, seven hundred and thirty-eight quadrillion, three hundred and eighty-one trillion, three hundred and thirty-eight billion, three hundred and twenty-one million, six hundred and sixteen thousand, eight hundred and ninety-six" are pleographically lectoral forms ("spell out") of these two numbers.

189.50.186.221 (talk) 02:21, 20 February 2025 (UTC)Reply

Maybe it's worth mentioning, that Z can be characterized as the smallest integral domain of characteristic zero, in similarity to the rational numbers Q being characterized as the smallest field (prime field) of characteristic zero. The section that states Z to be an integral domain could be extended as:

The lack of zero divisors in the integers (last property in the table) means that the commutative ring Z is an integral domain. In fact, every integral domain of characteristic zero includes Z, i.e. Z is the smallest integral domain of characteristic zero. PeterParker371 (talk) 15:21, 27 April 2025 (UTC)Reply

No reason of a restriction to integral domains. This is true for every ring (even non-commutative) of characteristic zero. Added in the article. D.Lazard (talk) 15:47, 27 April 2025 (UTC)Reply