Talk:List of types of numbers

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Euler Diagram

I believe that the Euler diagram showing the types of Real numbers is wrong since, from visual cues on the diagram, Real Number Set is not equal to the union of Rational and Irrational Number Sets. I'm too busy right now, so could someone fix that? — Preceding unsigned comment added by 130.158.126.130 (talk) 06:50, 2 June 2012 (UTC)[reply]

I would like to add that the Euler diagram also gives the utterly false impression that the set of irrational numbers is smaller than the set of rational numbers.--Lexy-lou (talk) 16:49, 20 July 2014 (UTC)[reply]

I deleted the diagram (at Image:Real numbers.svg) until a better one can be found or created. The image's talk page links to further discussion at Talk:Number#Rational.2Firrational --Theodore Kloba (talk) 21:29, 13 March 2015 (UTC)[reply]

Irrational.

Are we saying that Irrational numbers are not a type? A complement of a type need not be one, I understand, but the complement of the Rationals within the Reals surely should be listed.Cliff (talk) 18:11, 14 February 2011 (UTC)[reply]

Look at the page, Algebraic number, follow some of its links, and I hope you will see the folly of trying to diagram all of the different interesting groups and fields and sets of numbers, and their complements, on a single page. However, the sets that are defined on this page have special historical significance. They are the footsteps along the journey that began with our primitive ancestors sitting around a campfire counting their hairy toes to the invention of mathematics as a discipline worth studying in its own right. The information on this page is taught (or should be taught) to every kid in high school, and this page should be easy for those kids to find and understand. — Preceding unsigned comment added by 206.210.75.84 (talk) 21:58, 28 February 2013 (UTC)[reply]

No discussion of hypercomplex numbers

I noticed that hypercomplex numbers are not mentioned at all in this article. Should they be included? Jarble (talk) 20:53, 15 December 2012 (UTC)[reply]

Yes! I have included this type in the article. — Aetheling (talk) 19:44, 29 December 2012 (UTC)[reply]

No complex numbers?

Is there a reason why complex numbers are not mentioned under main types of numbers? 91.194.37.55 (talk) 20:19, 9 September 2013 (UTC)[reply]

Complex numbers were mentioned in a previous version of the article but were removed. I have restored them. Gandalf61 (talk) 12:17, 10 September 2013 (UTC)[reply]

Imaginary numbers

What about imaginary numbers? 62.253.137.86 (talk) 09:04, 10 September 2013 (UTC)[reply]

Imaginary numbers are a subset of complex numbers. I have restored the sentence on complex numbers. Gandalf61 (talk) 12:17, 10 September 2013 (UTC)[reply]

Whole Numbers

It states that natural numbers don't include 0, and wholes do, while I've always been taught the opposite, which frankly makes more sense. — Preceding unsigned comment added by 202.137.15.69 (talk) 06:44, 25 September 2013 (UTC)[reply]

Other number systems

Should this article also mention other number systems, such as integers modulo n or p-adic completions of the rationals? Depending on how broadly one defines "number", there could be many such systems. The two examples I've mentioned are used heavily in number theory, and hence are certainly relevant. Mgnbar (talk) 15:25, 5 October 2013 (UTC)[reply]

In https://archive.org/details/hypernumber_3_9 are some more. 190.114.50.75 (talk) 20:30, 12 September 2022 (UTC)[reply]

Other types of numbers

Would this be the appropriate page for other types of numbers (amicable, perfect, catalan, carmichael, etc.?) I can start on adding such links, if so. I couldn't find any other list pages with this kind of list.174.34.199.133 (talk) 23:35, 28 February 2014 (UTC)[reply]

See integer sequence. Gandalf61 (talk) 00:55, 1 March 2014 (UTC)[reply]

Thanks, should I add a link to Integer sequence here? 174.34.199.133 (talk) 19:06, 1 March 2014 (UTC)[reply]

Image – Rational/irrational

File:Real numbers.svg should be removed from page, or renewed.

See discussion in Talk:Number#Rational/irrational. – Laursen (talk) 12:32, 13 July 2014 (UTC)[reply]

So has anyone made a corrected version of that diagram? If so, then please go ahead substitute it into this article. Mgnbar (talk) 14:55, 13 July 2014 (UTC)[reply]

Real numbers

"Real numbers" is currently defined with "All numbers that can be expressed as the limit of a sequence of rational numbers," but this is false. For instance positive infinity can be expressed as the limit of the sequence of rational numbers 1,2,3,…, but it is not a real number. Instead we need to go with something like "Archimedean complete totally ordered field" (as translated into common language) or "Dedekind cuts" or some other equivalent definition. Leegrc (talk) 14:51, 23 July 2015 (UTC)[reply]

Because the definition is technical, and this article is just a list, maybe we should just omit it. Maybe we should leave the work to Real number. Mgnbar (talk) 15:22, 23 July 2015 (UTC)[reply]

Zero in Natural Numbers

Refer to Talk:Natural number for discussion of inclusion of zero in Natural numbers. IveGoneAway (talk) 13:59, 28 September 2016 (UTC)[reply]

There is an international standard for natural numbers with the inclusion of zero. That standard should be presented first in this list whereas the alternative without 0 should be presented second, as it is in Natural number. There does not seem to be an active discussion on the inclusion of zero in Talk: Natural number, but this change would reflect the order of presentation in Natural number. Otherwise, it appears these two pages on the same mathematical structure are in conflict. 2601:18C:CC01:4F30:ECBD:B16E:89D9:D956 (talk) 17:03, 15 March 2020 (UTC)[reply]

There is no international standard for including 0 in the natural numbers. Many texts include 0 and many do not. (My personal preference is to include 0 in the natural numbers, but my personal preference does not matter.) Mgnbar (talk) 17:09, 15 March 2020 (UTC)[reply]

The standard ISO 80000-2 listed on Natural number is an international standard by ISO, this standard is also reflected as part of IEC. Zero is included in the Natural numbers in that standard. 2601:18C:CC01:4F30:ECBD:B16E:89D9:D956 (talk) 17:12, 15 March 2020 (UTC)[reply]

Thanks for your response. I understand that ISO has a document, which they call a standard. However, this standard is not at all obeyed by the real world, which is what Wikipedia is about.

So as to avoid two parallel discussions, I propose that we put this discussion on hold, focus on Talk:Natural number, see what happens, and then update this page accordingly. Regards. Mgnbar (talk) 10:56, 16 March 2020 (UTC)[reply]

The ISO is subscribed to and adhered to by over 83% of the countries in the world. Talk:Natural number no longer has a non-archived discussion about zero's inclusion. Natural number presents this inclusion argument first, citing the International Organization for Standardization's standard. It's clear at this point that you are not discussing this in good faith. 2601:18C:CC01:4F30:8100:6933:26DA:FAA0 (talk) 03:54, 17 March 2020 (UTC)[reply]

I am discussing in good faith. I've been editing Wikipedia for 15 years, always in good faith.

I made a mistake in referring to Talk: Natural number's discussion. I was accidentally looking at an archived version. You are right that there is no current discussion. Sorry.

I understand what the ISO is. We can continue to argue about how much weight it has. But let's not, because we really have very little dispute here, I think...

Concretely, do you simply want to list the including-0 definition first and the excluding-0 definition second? Then go ahead! If, meanwhile, you want to beef up the references for both, then that would be great. :) Mgnbar (talk) 11:32, 17 March 2020 (UTC)[reply]

Whole numbers

In the part about natural numbers, my issue with the mention of whole numbers is that the cited sources do not clearly state the relationship between the natural and whole numbers. Mgnbar (talk) 13:53, 20 January 2020 (UTC)[reply]

Today's edits

Today's edits continue to be counter-productive. The quickest fix is just to revert to the last good version, but since it was requested here is a list of some of my current objections:

The section title "Main types" is not great, but "Constructed sets" is worse, because that can be taken to mean something else, and the examples here can be defined without construction anyway (e.g. axiomatic definition of the reals).
It doesn't make sense to mention indeterminates in the rational number description. Yes, sometimes indeterminates end up being rational. At other times they don't. In any event, the way the number is written is not the number itself.
It's not clear why imaginary numbers were deleted.
In complex numbers, b does not represent a quantity of i, unless we mean -i b of i, and I hope we don't.
Hypercomplex and p-adic numbers appear to be listed as sub-types of transcendental numbers, but should not be.

Mgnbar (talk) 23:21, 25 September 2023 (UTC)[reply]

thank you very much! i'm really intent on learning better ways to write and frame these technical things, i try to be bold in other words, but that's why i was as vocal as i was, i hope it doesn't come off the wrong way. i had thoughts on most of these points while i was writing, but i won't trouble you further with them, since i trust you know better than i do. Remsense (talk) 23:36, 25 September 2023 (UTC)[reply]

Thank you for being bold and taking constructive criticism so well. Happy editing. :) Mgnbar (talk) 00:23, 26 September 2023 (UTC)[reply]

Computer based numbers

Though there is a brief discussion of binary, octal and other number systems particularly relevant to computers, there is no mention of number types as used in programming language, such as int, long int, float, double etc.

For many people computers and the types they manipulate are an important introduction to the discipline of working with numbers and their pragmatic implementations. Things like the max and min values of int, the accuracy of floating point numbers could usefully be mentioned, ideally pointing to an article relating to those uses and issues in more detail. Another important feature of these pragmatic number representations on a computer is the use of exceptions and exception handling. This allow programmers to write logic like: speed = distance / time where all variables are floating and allow problematic situations like a time of 0.

Exceptions and exception handling allow such ( often rare) situations to be handled elegantly elsewhere without creating complex checking code prior to using the numbers. This is especially valuable when there is no simple way to handle such exceptions in the middle of a complex calculation or algorithm or other process. CuriousMarkE (talk) 08:18, 8 October 2024 (UTC)[reply]

I agree with the basic idea. It makes sense to mention floating-point numbers such as IEEE 754. It makes sense to mention signed and unsigned integers of various bit sizes.

But keep in mind that this article is just a list. It's not supposed to have big exposition. Maybe I lack imagination, but I'm having trouble imagining how exception handling will fit into the list. Mgnbar (talk) 21:45, 8 October 2024 (UTC)[reply]

Re exception handling.

Consider signed char, unsigned char, signed int in C.

2-4 when using unsigned char will not give the expected result since C just wraps around.

However, C compilers can create more comolications, see:

https://www.gnu.org/software/gnulib/manual/html_node/Wraparound-Arithmetic.html

Providing the ranges and computational limitations are understood, then these implementations can be treated like integers.

But those limitations are significant.

The big difference is when an exception is raised, or should be raised. If the result of an operation is not in range, then an exception is raised, or un unexpected result is likely.

Thus, unlike mathematical integers, the user has to be aware whether the values and operations could cause an exception or other awkward behaviour, like wraparound.

If they are sure they won’t encounter such isssues, no issue. If it isn’t important to the general use of the program and generic exception handling, like gracefully halting the program with simple error information, is adequate, then again no issue. This latter situation is useful in early development when the basic logic needs sorting out for easy use cases.

Otherwise, some awareness of the role of the valid number range of the computer number representation and checking of the input data and associated error handling or exception handling is required.

I believe information at this level, with some good examples, is appropriate here. CuriousMarkE (talk) 05:52, 2 November 2024 (UTC)[reply]

Thanks for your reply. This article should link to other articles, such as Integer overflow, where all of that is explained. This article should not reproduce that exposition. Regards, Mgnbar (talk) 13:49, 2 November 2024 (UTC)[reply]