# Definition talk:Number

Why this change?

$\N \subseteq \Z \subseteq \Q \subseteq \R \subseteq \C$

from

$\N \subset \Z \subset \Q \subset \R \subset \C$

?

The subsets are definitely proper as $\N \ne \Z$, for example. --prime mover (talk) 17:31, 12 October 2012 (UTC)

Don't know; I felt like changing something, I guess. We have been systematically eliminating $\subset$, for the better IMHO; if you want to stress strictness, please use $\subsetneq$. --Lord_Farin (talk) 17:36, 12 October 2012 (UTC)
Does $\N \subsetneq \Z \subsetneq \Q \subsetneq \R \subsetneq \C$ look right to you? Personally, I liked the way it was before. Also, you might want to make a site-wise note of it on the proper subset definition page if you plan on doing this change throughout PW. --Jshflynn (talk) 18:44, 12 October 2012 (UTC)

My view is:
a) $\N \subseteq \Z \subseteq \Q \subseteq \R \subseteq \C$ while being technically accurate is weaker than $\N \subset \Z \subset \Q \subset \R \subset \C$
b) A page of this general accessibility can get away with the "$\subset$" as it does not matter whether it is interpreted as $\subsetneq$ or $\subseteq$.
In general I am in favour of $\subset$ being replaced as and when it's encountered, but on this page I think we can get away with it. Feel free to argue in either direction. --prime mover (talk) 18:53, 12 October 2012 (UTC)

## Prime numbers

The number $-3$ has exactly two positive divisors: $1$ and $3$. By your definition, Prime mover, master of all brilliance, $-3$ is prime. Thus the statement that the first few primes are $3, 5, 7, 11, 13$ is wrong. Rather, there is no first prime number. Unless you intend the identities of those two divisors to be part of the definition, O Brilliant One. What the heck is your problem with just saying they're natural? --Dfeuer (talk) 22:02, 28 March 2013 (UTC)

Yes, $-3$ is prime. --prime mover (talk) 22:06, 28 March 2013 (UTC)
It's a prime element in the ring of integers; it's not a prime number. --Dfeuer (talk) 22:11, 28 March 2013 (UTC)
Sources? --prime mover (talk) 22:15, 28 March 2013 (UTC)
Look at it like this. Some sources define prime numbers to include negative numbers. Some do not. To say that $\mathbb P \subsetneq \Z$ is true whichever definition you use. To say that $\mathbb P \subsetneq \N$ is not. --prime mover (talk) 22:23, 28 March 2013 (UTC)
I also direct you to Definition talk:Composite Number where the discussion has already been had. --prime mover (talk) 22:26, 28 March 2013 (UTC)
I note that Definition:Prime Number has not yet caught up to Your Awesome Wisdom. --Dfeuer (talk) 22:38, 28 March 2013 (UTC)
Source: Knuth 1.2.1. --Dfeuer (talk) 22:41, 28 March 2013 (UTC)
PM: please verify that your venerated source defines "prime number" so, rather than "prime integer". --Dfeuer (talk) 22:45, 28 March 2013 (UTC)
cba--prime mover (talk) 22:51, 28 March 2013 (UTC)

Now quit arguing. --Linus44 (talk) 22:27, 28 March 2013 (UTC)

What a despicable, perverted display of childishness. I wish I hadn't chosen this link to check up on the site. Yugh. I'll quickly leave now, before I completely lose my temper. — Lord_Farin (talk) 23:18, 28 March 2013 (UTC)
I apologize, Lord_Farin. I've had a stressful week and took it out on PM. --Dfeuer (talk) 00:44, 29 March 2013 (UTC)

## Other numbers

We could add another section, appropriately titled. As long as we don't add so much clutter to a page which is already busier than it needs to be. Adding them into the Also see might be appropriate, which we might split into sub-categories for these more-or-less artificial constructs which are only classified as "numbers" because they are called "numbers". However we call attention to them, it would probably be best if these constructions were kept separate from the main $\N, \Z, \Q, \R, \C$ classification which was the original intention of this page. --prime mover (talk) 22:40, 8 July 2020 (UTC)
I've never heard of anybody refer to "traditional numbers" so I'd rather we did not use that terminology. As for "extended numbers", that term is used for $\R \cup \set {-\infty, \infty}$ ("extended real numbers") so that's also doubtful. I'm also reluctant to create a paradigm which results in huge colossal quantities of work, which would be a danger if we were to change our default terminology from "Number" to "Traditional Number".