|WikiProject Mathematics||(Rated Start-class, Mid-importance)|
n(R) equal to Aleph 0?
Now it seems that the number line is, in essence, the set of the reals. The cardinality of the set of the reals is NOT the "simplest and smallest measure of infinity" or whatever - or at least, I thought it wasn't. I thought that the simplest and smallest degree of infinity was the cardinality of the natural numbers (equal to n(Z) and n(Q)). Am I correct? I will change it, and if I'm wrong, someone else will change it back. 220.127.116.11 08:23, 15 September 2006 (UTC)
- he principle involved with the number line is to change the set of real numbers into an ordered set so that everybody agrees as to the magnitude of each number. And counting then becomes the step by step establishment of elements of any other set of items with the ordered set of numbers with the last related number being the quantity in question. WFPM (talk) 13:01, 9 November 2008 (UTC)
From my textbooks, a number line should have only one arrow, marking the direction of the positive numbers; not two arrows. —The preceding unsigned comment was added by Yazewu (talk • contribs) 02:28, 8 January 2006.
- That's an uncommon convention, but you're welcome to add it to the article, if you cite the reference! Melchoir 01:19, 9 March 2006 (UTC)
- I have also seen this convention used - on a cartesian line or plane, the arrows indicate the direction of positive. However, the convention referred to in the article is simply that of the line continuing to infinity, in which case it should be present on both the left and right ends of the line.
- 18.104.22.168 08:25, 15 September 2006 (UTC)
Can the number line be curved so that +infinity and -infinity meet?
- Take a look at the real projective line, which joins the real numbers with an unsigned infinity. As far as practical/useful/meaningful constructions, this probably comes as close as possible to what you want to describe.02:47, 18 October 2007 (UTC) —Preceding unsigned comment added by 22.214.171.124 (talk)
- How come we have a big long history of the Pythagorean theorum and none on the Number line. The Number line must have a reportable history, (I learned about it about 40 years ago), and use it and the Pythagorean theorum to visualize how to find the square root of any integer number. WFPM (talk) 14:25, 4 November 2008 (UTC)
"All of the real numbers from negative infinity to positive infinity"
Is that accurate? It seems prone to produce confusions about infinity - infinity isn't in the set of reals, and I don't think infinity can reasonably be placed on a line with the reals (what number would it come after?). Can we just say "all the real numbers" and leave infinity out of it? VoluntarySlave 03:16, 31 January 2007
- Infinity is not a number. It is a condition of being greater than any previously assigned number, however large. WFPM (talk) 13:05, 9 November 2008 (UTC)
Division as repeated subtraction?
From the article: "It is used sometimes to teach multiplication as repeated addition, and division as repeated subtraction." Division is not repeated subtraction. I'll remove this; re-add if you disagree. 03:00, 18 October 2007 (UTC)
Suggestions for improving article
The number line is an important concept in basic mathematics, making this a fairly important article. In case anyone is interested in working on it, here are some suggestions for content that could be added to this article:
- A geometric discussion of addition and subtraction of real numbers using the number line, ideally including pictures
- A basic discussion of how left and right correspond to less than and greater than, as well as how distance corresponds to the absolute value of the difference
- A short discussion of how the rational numbers fit onto the number line. This might include, for example, a picture of the interval [0, 1] with the positions of several fractions shown.
- A discussion of transformations of the number line, e.g. addition as translation, negation as reflection, and multiplication as scaling
- A discussion of intervals and rays, and how they appear on the line.
No "History" section?
This article really needs a section on the history of the number line, citing (among other things) the earliest documented cases of people using an imaginary line as a tool for visualising the relationships between different numbers. I visited the article in the hope of learning about the history of the concept, as most Wikipedia articles on mathematical topics include a "History" section. The number line seems intuitively obvious to us now, because it's taught in every school, but for how long has it been so? 126.96.36.199 (talk) 11:33, 25 April 2013 (UTC)
- In a European context, this goes back to the beginnings of analytic geometry in the work of Pierre de Fermat and Decartes. Tkuvho (talk) 13:39, 25 April 2013 (UTC)
The figure currently shown in the article shows the positive numbers in a different color than the negative. However, the whole point is to view both types of numbers as being elements with equal rights. The figure may be more confusing than helpful. Any suggestions? Tkuvho (talk) 16:53, 3 February 2014 (UTC)
- It also shows the number line with two arrowheads, which is an idiotic convention used in American schools. A line without arrowheads continues infinitely in both directions - this is the traditional geometric rule; if you want to depict a ray or a segment then use either dots or strokes at the end of the segment. The number line must have only one arrowhead, which denotes direction in which numbers grow, for example a horizontal line with arrowhead on the left means numbers increase to the left, not to the right - this is how it is depicted and taught in Europe and in many (most?) Asian countries. --Mikus (talk) 01:08, 6 January 2015 (UTC)
- I may be misunderstanding you, but how then, do you differentiate between a line that increases negatively, and a line that simply ends? Is it necessary to end every line with an open or closed dot, or is there some other convention? 188.8.131.52 (talk) 21:55, 7 April 2015 (UTC)