Talk:Division (mathematics)

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needs some history A vital article.

Perhaps we should have some explanation of restoring and non-restoring division algorithms?

(Edit: yes, please! I can't find an explanation anywhere. Please, Obi-Wan-Wiki, you're my only hope...)

Should there be any reference to a military unit sense?

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Should we write a division algorithm?

Contents 1 Let's have the correct definition of division! 2 Integer division? 3 computers 4 Article (or section) request

[edit] Let's have the correct definition of division!

Intermediate Algebra by Barnett and Kearns has the actual definition of division and the explanation as to reason for division by zero is not defined:

"We say that a divided by b equals c if and only if there exists a unique value c such that b times c equals a."

Division by zero (b=0) is not defined because if a is nonzero, c doesn't exist, and if a is zero, c is not unique.

B.Wind 21:38, 24 December 2005 (UTC)

The division by zero rationale is useful, I agree, and maybe we can work it into the article. The information in the first statement (the "definition"), though, is already adequately covered in the article intro. Also, as phrased above, it is not really a definition in the sense of "Division is…"; rather it makes a statement about something "we" say in relation to division. So I greatly prefer what is in the intro right now.

There is also no "we" in an encyclopedia, despite the fact that this article and many other math related articles often egregiously violate this principle. Although it is hard to break the habit of using the lecture style when discussing technical subjects, at least make an attempt to make important declarations without directing the reader's attention ("note that"/"notice how"), giving the reader advice ("one should"/"it should be noted that") or referring directly to a speaker or listener ("we say that" etc.).—mjb 18:01, 17 June 2006 (UTC)

[edit] Integer division?

In the section "Division of Integers", Patrick recently replaced

Give the quotient as the answer, so . This is sometimes called integer division.

so that (with some copyedits by Oleg Oleg Alexandrov) it read:

Two versions of what is sometimes called integer division:

(a) Apply the floor function to the quotient, so .

(b) Truncate the quotient, so .

These coincide if the integer to be divided are positive.

I've reverted for a couple reasons. First of all I can't infer the general rule from the example given in (a). For example what is 26/10 equal to? 3 or 2? Also why introduce -26/10, when the original example was 26/10? (Can someone supply a source for this definition of integer division?). Secondly (b) is a rewording of the original, but I think the original is better. And again why change the sign of the example? Finally I don't know what is meant by "These coincide if the integer to be divided are positive".

Paul August ☎ 20:45, 16 June 2006 (UTC)

By "These coincide if the integer to be divided are positive" I meant the two definitions (a) and (b). But I agree that the whole thing doesn't make any sense. Oleg Alexandrov (talk) 21:04, 16 June 2006 (UTC)

[1] and [2] say that we have to truncate a negative quotient, while [3] says we have to apply the floor function. See also [4]. --Patrick 07:31, 17 June 2006 (UTC)

Thanks Patrick for providing these sources, I will add some of these to the article, when I get a chance. Your new edit is much better so thanks for that also. Besides apparently Mathematica, and Python, are there any other examples where integer division is implemented by rounding toward negative infinity? Paul August ☎ 18:04, 17 June 2006 (UTC)

There's an interesting comment on this by Italo Tasso on this page, which suggests that Perl also may have this. The treatment of the quotient, which is naturally the main focus of this article, is intimately related to the remainder and/or modulo congruence value (see also Modular arithmetic#Remainders). I believe some programming languages in fact provide both types of remainder. The GNU multiple precision arithmetic library provides both kinds of quotient. -R. S. Shaw 05:17, 18 June 2006 (UTC)

[edit] computers

why is there no divide key on keyboards? Wtatour 23:57, 28 June 2006 (UTC)

Historically, both "/" and ":" have been used as division signs. Personally I only use the latter when setting up informal division calculations. So, it depends on what you mean by "divide key". --Frodet 16:09, 30 September 2006 (UTC)

[edit] Article (or section) request

I think "Dividing by 0" is a valid discussion topic that worth at least a section on this article. Or even expland into a full article that consist of varies methods of proving that "Dividing by 0" is undefined. Lightblade 17:24, 16 November 2006 (UTC)

There's a link to Division by zero at the end of the lead section. I agree that it should have a section in this article as well; why don't you try writing it? Melchoir 19:02, 16 November 2006 (UTC)

Thanks for the link! I didn't see it down there. Lightblade 21:38, 16 November 2006 (UTC)