Talk:Algebra/Arithmetic

From Talk:Absolute value
IIRC, absolute values of complex numbers isn't something typically covered in Algebra I and it's more something for Algebra II or Trig(coupled with De Movire's Theorem maybe?) Etothex 03:37, 20 Sep 2003 (UTC)


 * The explanation here is very basic. A more thorough explanation will be explored at Algebra/Complex Numbers; perhaps this will serve as motivation to read up on complex numbers? Dysprosia 11:03, 20 Sep 2003 (UTC)


 * It's nice IMO to have something a little advanced in a book to inspire students to learn new stuff.Absolute value of real numbers is a trivially easy, we need to inspire the bright ones. Theresa knott 11:47, 20 Sep 2003 (UTC)

Discussion
use a midscript * that is in the middle. don't use a plain astertisk.

Do you really think that subtraction is a binary opperation? In fact, addition is an abelian (semi)group (depends if you have already negative integers or not). Minus is the the _unary_ operation of inversion, hence a+(-a)=0, where 0=zero is the unit element of the (semi)group. In the case of addition one should hence write a+(-b) and not a-b. This solves the commutativity problem, since a+(-b)=(-b)+a. The notiopn a-b can then be introduced as a shorthand. While I would not recommend to introduce abelian groups at this level, I would strictly object against the introduction of a binary operator called minus, July 26, 2004 BF.

That picture of the number line is really bad--it would be much simpler just to use an image.

I have made an image and fixed the problem. It now looks beautiful. :-) H Padleckas 12:51, 11 Jul 2004 (UTC)

Paul - What are we trying to do here with this page? There doesn't seem to be a comprehensible focus on the page. My take on it is that we're trying to create a maths textbook that can be used to teach someone arithmetic - if that's the case then what are all those useless bits and pieces about subtrahend and Numerical Axioms doing in there?

On the other hand, if we're trying to document Arithmetic for someone seriously studying the root of mathematics, why have exercises asking for the solution of 5-3?

It doesn't make sense that exercises as simple as 5-3=? would be on the same page as words like subtrahend.


 * It was my impression that the page was for a brush-up lesson on the basics of arithmetic necessary for using algebra. Subtrahend (and the other higher-level stuff) would therefore be the extraneous information. - Jonel

Whoever posted anonymously made a very good point about the order of operations. I've cleaned it up a little; if you think it needs more work feel free to alter it. As for the etiquette, for the most part if you see something that needs to be fixed you should just go ahead and fix it. If you're unsure, put a message in this talk page. Jonel


 * Actually - that was me before I registered as a user :) The editing looks fine to me. I tihnk I'm going to enjoy working on this project! - Paul

I don't think that this section is in keeping with the idea of this page, but it might be useful on another page for more advanced work. So I will just leave it here on the talk page for now. Jonel

"Absolute Value" of Complex numbers
For complex numbers, the absolute value or modulus presents us with a different concept. A number in the Argand plane has a rotation from the real axis through angle &theta; and a distance away from zero, r. By using the Pythagorean theorem and a bit of trigonometry, we can generalize the complex number to be a triangle, and we obtain that the modulus is the same as the real value squared plus the imaginary value squared (See Algebra/Complex Numbers for more detail).


 * z2 = Re(z)2+Im(z)2

then
 * z|= &radic;(Re(z)2+Im(z)2)

It is important to note that if z has imaginary part zero; ie z is purely real, this method is equivalent to finding the absolute value as well.

Previous section?
Under Addition, a "previous section" is referred to. There is no previous section. This is the first section of Math. H Padleckas 12:51, 13 May 2004 (UTC)
 * I agree. I fixed it. --MathMan64 21:52, 2 September 2005 (UTC)

BODMAS
Hello. I'm using this Wikibook to come to grips with maths in english. In my native language (Dutch) I'm pretty clued up, but the language barrier is keeping me from understanding a lot of maths-related stuff in english. Just now I stumbled upon something which I can't quite understand:

"There are a number of different abbreviations for memorizing the order. PEMDAS, BEDMAS and BODMAS (B is Brackets) are common." I can't figure out where the O in BODMAS comes from? Care to enlighten, anybody?

[edit] The "O" stands for Orders (ie Powers and Square Roots, etc.) The "O" has also been taught simply as "OF"; Brackets of Divison etc.

Thanks to all contributors for taking the time to write all this. Perhaps I'm a bit simple-minded, but I feel the book could do with some graphics (even non-functional graphics), both to break the text apart in more managable chunks, and to make it more appealing from a visual point of view.

Order of operations
I feel that this page is not the correct place to introduce anything to do with negative numbers, such as -22. This important concept should be introduced after the multiplication of integers. I would rather it not be a subtraction problem from zero, but a multiplication by negative one. --MathMan64 22:48, 2 September 2005 (UTC)

Long multiplication?
Can there be some information about how to multiply large numbers, say 34 * 281 or whatever.

addition and the other operations too, for that matter. this wikibook gives excercises for them, but does not explain the method of solution. 206.15.236.254 16:57, 20 April 2006 (UTC)

Exercises
I think it would be good to add exercises to each arithmetic section. I performed all exercises so far and found some holes in my understanding that I would not get from the explanations alone. Particularly, start from simple to advanced within 25 problems so the student can get a real feel for what they are lacking. I will create some of my own and add it here in a couple of days if no one has any objections.:) ---Irishboy0 01:27, 21 September 2006 (UTC)#--Irishboy0 01:27, 21 September 2006 (UTC)

missing pages with problems
I marked this page fair for completeness due to the missing pages when you try to go to the problems for each category on this page. only the pages for addition and subtraction exist. Kweeks (talk) 11:21, 6 September 2010 (UTC)

"Addition"
Why in quot.marks? Cause the issue is not about addition while the passage is out of there: "To define the number one is a rather difficult task, but we all have a good intuitive sense of what "oneness" is."

O'k, not a very good way... Know what I think? I think that we can′t define oneness without quantity. Moreover, the concept of quantity is of the premises to the oneness not otherwise. No oneness does exist without a quantity prior to that. The quantity is a natural concept — then somebody, planning to organise the surrounding, chooses the units. You may argue that there is a natural concept of oneness - when considering some indivisible objects — for example humans etc. (apples etc.). Somebody could say that either humans or, especially, apples can be divided. To those, it will be recalled that the objects should strictly retain their immanent parameters so as to remain being considered equal or comparable in the same way. Well, it was an interlude. So... Somebody says "what about 'natural objects'?" — thus resolving the phantom paradox: saying "natural". Now, I agree that there are objects which may imply some natural oneness. BUT THEY ARE ONLY "NATURAL", COUNTABLE OBJECTS. Linguistics seems giving the best answer to solving such ambiguities: remember the classes of nouns in English:) So, this way we have NATURAL DICHOTOMY between the countable and the uncountable. So we should choose the way of approach to our dilemma: either we introduce here in "Arithmetics" the natural numbers first — or we're defining the quantity as a prior to any units perceptional concept... Lincoln J. (discuss • contribs) 17:44, 19 January 2013 (UTC)

Logarithms
It is arguable that the introduction of digital technologies has largely replaced the need for logarithms at this level of mathematics. If so, is this section necessary? Colinf (discuss • contribs) 22:22, 30 July 2014 (UTC)