Definition talk:Number

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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)