Template talk:Classification of numbers

Errors and misinterpretations

Period (algebraic geometry) suggests that the algebraic irrational real numbers are a subset of the real irrational periods. Is that right? The point of this tree diagram is to depict such subset relationships, right? But it doesn't depict this one correctly.

In the complex numbers, the real numbers and the imaginary numbers are not disjoint. Their intersection is {0}. So the tree seems not to depict this relationship correctly.

Maybe I'm misinterpreting what the tree is supposed to depict. In general, I'm worried that readers, who don't already know this content, will misinterpret the tree. For example, the tree might reinforce the common misconception that the complex numbers are partitioned into the real numbers and the imaginary numbers. Mgnbar (talk) 12:40, 9 October 2025 (UTC)

There are several errors in this template

• Presenting imaginary numbers as disjoints from real numbers is not really an error: When one says that every complex number can be uniquely written as the sum of a real number and an imaginary number, you must include 0 in the imaginary numbers, but when one says "let ⁠$x$⁠ be an imaginary number", this excludes generally 0. Since imaginary numbers are rarely considered for themselves, except as imaginary parts of complex numbers, I would recommend to remove this entry, or, better, to replace it with "non-real"
• Rational numbers, fractions and repeating decimals are exactly the same set of numbers. They must belong to the same entry.
• Integers form a subset of both finite decimals and finite binary. This must be clear on the picture
• Irrational algebraics form a strict subset of the irrational periods, and the irrational periods that are not algebraic form subset of the transcendental numbers. Making this clear would require a change of the structure of the template. So, I suggest to remove the entry on pediods, which, in any case, seem too technical for this template.

D.Lazard (talk) 14:32, 9 October 2025 (UTC)

Setting aside any disagreement about 0's being imaginary, your objections are mostly about a certain interpretation of the tree. For example, are the branches coming off a set supposed to partition that set? When "repeating decimal" is under "fraction", does it mean all repeating decimal numbers, or all repeating decimal fractions? Also, what exactly does "fraction" mean here? That's why I'm trying to get clarification about the original intent.

My current opinion is that this tree diagram does more harm than good. Mgnbar (talk) 15:20, 9 October 2025 (UTC)

I agree, and I have replaced boldy the diagram by a correct image. Feel free to change it again with a correct diagram or a more complete image. D.Lazard (talk) 16:07, 9 October 2025 (UTC)

@D.Lazard@Mgnbar Hi, to be honest, I am not a mathematician, but I really love mathematics. In my opinion, inaccurate introduction of "classification of numbers" can be very helpful, because it provides a common sense (main idea). According to Occam's razor, unlike computers, for humans, inaccuracy of definition is not only acceptable but is recommended. Finally, I propose to rewrite the template, to be something like this Japanese version. Thanks, Hooman Mallahzadeh (talk) 04:48, 11 October 2025 (UTC)

Something like Newton's laws of motion

At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass

This law is not true for high speeds (near the speed of light), but it is used as a common sense. I mean, this law is inaccurately used. Hooman Mallahzadeh (talk) 05:56, 11 October 2025 (UTC)

In here, the "Classification of numbers" is inaccurately useful. Hooman Mallahzadeh (talk) 08:12, 11 October 2025 (UTC)

In mathematics, inaccurate definitions may be useful in the lead or in introducing sections (Context, Motivation, etc.), but are misleading if it is not clear that there is an accurate definition (otherwise, they would not be mathematical definitions). T.he previous diagram is unacceptable because it can easily misinterpreted, and, also, because there is no reasonable interpretation that does not contains errors (see my above analysis of the diagram). A misleading diagram is definitively not useful, unless if you want to give to non-expert readers a false idea of what is mathematics. D.Lazard (talk) 08:18, 11 October 2025 (UTC)

@D.Lazard Ok, and thank you for your response. In the year 2021, I had taken this template from this Spanish version, which was created in 2009 and is used till now. So I am not the original writer of this template, I am only a translator. If you are sure that this sort of classification is not acceptable, and there is no way to correct that, please declare other 7 Wikis (Japanese, Spanish, Hindi, Turkey, etc.) to remove that. Thanks again. Hooman Mallahzadeh (talk) 09:37, 11 October 2025 (UTC)

As you may know, translating math can be difficult. For example, the German word Körper, which usually translates as "body", instead translates as "field" in a math context. Maybe that's part of the problem? Or maybe those wikis also have mistaken tree diagrams.

The Newton's law example is not a helpful analogy. Attempts to translate reality into math are inherently imperfect, approximate, and temporary. But once one is working in math, one can be exact about that math. Regards, Mgnbar (talk) 13:52, 11 October 2025 (UTC)

What's D?

The new diagram is prettier than the old one, and contains more information, so I like it — mostly. But what does it mean by $\mathbb {D}$? I've never seen that notation. Mgnbar (talk) 13:26, 23 October 2025 (UTC)

Hi, it is Decimal fractions:

Decimal fractions are the rational numbers that may be expressed as a fraction whose denominator is a power of ten.

Mentioned in the caption of figure in «Number» article. It is also new for me. I think this notation is never used in other books. Hooman Mallahzadeh (talk) 15:33, 23 October 2025 (UTC)

Thanks. Is there a reliable source that attests this notation?

Setting aside the notation, I doubt the notability of this set. It is dependent on the number 10, which is rather arbitrary, as far as math is concerned. Other bases would lead to other notions of $\mathbb {D}$. But I can be convinced. Mgnbar (talk) 17:09, 23 October 2025 (UTC)

If ⁠$\mathbb {D}$⁠ is mentioned, then the quadratic numbers, the constructible numbers, the algebraic numbers, the computable numbers, and probably several others should be mentioned. The caption talks of main number systems. Certainly, the decimal numbers (and the other number systems that I have mentioned) are not are not among the main number systems. Moreover, the fact that 0 appears as an example of a natural number is clearly confusing.

So, I will restore the previous image. If somebody is able to find an image that is prettier and not controversial, be free to replace the uncolored image. D.Lazard (talk) 20:45, 23 October 2025 (UTC)