Here's another perfect example of a topic that could benefit from a plainer-language, if inexact, definition given first (and billed as "rough" or "inexact")--followed by the more precise, but harder-to-understand, definition. --Larry Sanger 17:47, 31 March 2007 (CDT)
For example (I'm not going to actually edit the article--this no doubt needs worthsmithing):
- A divisor of a number, roughly speaking, "goes into" the number evenly, with nothing left over (no remainder). For example, 2 is a divisor of 4, because 2 goes into 4 two times, with nothing left over. But 2 is a not a divisor of 5, because 2 goes in 5 2.5 times.
- More exactly, given two numbers d and a, d is a divisor of a if, and only if, a divided by d equals an integer, that is, a number without fractions. So if d = 5 and a = 15, then d/a = 3, and so d is a divisor of a.
- Even more exactly and formally, given two integers d and a, where d is nonzero, d is said to divide a, or d is said to be a divisor of a, if and only if there is an integer k such that dk = a. For example, 3 divides 6 because 3*2 = 6. Here 3 and 6 play the roles of d and a, while 2 plays the role of k. Though any number divides itself (as does its negative), it is said not to be a proper divisor. The number 0 is not considered to be a divisor of any integer.
Again, what I'm aiming at here is an explanation for people who don't already know what "divisor" means. Anyone who doesn't know what "divisor" means won't be able to understand the first paragraph of the article at present, which we should be able to agree is a problem. ---Larry Sanger 09:53, 3 April 2007 (CDT)-Larry Sanger 09:53, 3 April 2007 (CDT)
- I agree with the above, as does at least one other person, see my talk page. I'm all for anyone putting that stuff in at top of article asap. I will be rather busy elsewhere till 17th.Rich 17:11, 3 April 2007 (CDT)
"proper divisors" comment
1 and -1 might be proper divisors, contrary to the current version. I think they're called trivial divisors instead. My evidence: The statement "6 is perfect because it is the sum of its proper divisors 1, 2, and 3" is everywhere.Rich 20:09, 31 March 2007 (CDT)
- I'll fix it. Thanks. Greg Woodhouse 20:21, 31 March 2007 (CDT)
- Man I'm over the hill! By my quote about 6 above negative numbers like -1 or -3 can't be proper divisors of 6. Sorry.Rich 12:37, 2 April 2007 (CDT)
"Fearless Symmetry" is certainly a fascinating read, but really out of place in this article. (It's an introduction to the ideas behind the proof of Fermat's last theorem for non-specialists.) I was a bit, well, ebulient, in placing it here. I'll probably use it elsewhere, such as in an article on reciprocity laws. Greg Woodhouse 13:22, 2 April 2007 (CDT)