Talk:Arithmetic

More elementary?

Paul, it is a good idea to have a non-formal article on arithmetic. What do you think about making it even more elementary? (The more formal treatment can be left to the articles on rational and real numbers, etc.) Most, if not all, mathematicel jargon could be avoided. Take e.g.:

"Two (or more) numbers can be added (denoted by +), and the result is again a number. This addition does not depend on the order in which it is performed. For example, 3 + 5 ≡ 5 + 3 (= 8)."

It is not necessary to use "binary", "commutative", "field". Even "real number" can be replaced by "number".

Peter Schmitt 23:37, 5 January 2010 (UTC)

Please go ahead, it is a Wiki, remove all learned terms. I was not quite happy, indeed, with being somewhere in the middle between informal and formal maths. But I found it useful to have a symbol for the set of all (real) numbers, and then I thought why not use ℝ? And then I thought why not mention its official name? And so one thing led to another. --Paul Wormer 06:15, 6 January 2010 (UTC)

Sure, it's a wiki. But why not first check (and discuss) the intentions? You may be right about using the ℝ (From where did you get the non-TeX ℝ? (Is it safe on all browsers?)) and perhaps even using "real" does not hurt though elementary arithmetics only uses rational numbers. But you seem to agree that "commutative" etc. is not needed here. --Peter Schmitt 01:13, 7 January 2010 (UTC)

The ℝ is OK on IE-8, Chrome, and Firefox, its code is: ℝ (edit to see it). I don't have a deep feeling for the article, I saw that it was on the most wanted list, and then off the top of my head I wrote a few lines. Whatever you change is fine by me. The idea that it should be readable by a non-mathematician is good one, after all everybody [over 50 ;-), people under 50 need a calculator] can do arithmetic. With regard to the irrationals, that is debatable, do roots belong to arithmetic? I don't know. In elementary school I learned the order: MVDWOA, where the M stands for "machtsverheffen" (macht = Potenz), and the W for "worteltrekken" (wortel = Wurzel), which makes me suspect that roots belong to arithmetic. --Paul Wormer 08:19, 7 January 2010 (UTC)

In the olden days (about a century ago) arithmetic exams included extracting square roots by hand. Peter Jackson 11:17, 7 January 2010 (UTC)

I know (I can do it, slowly, but I do not like to do it :-) but neither extracting the square root of two by hand nor by pocket computer (or by a supercomputer) gives you the true root. "Elementary" (or numerical) arithmetic always uses rational approximations. --Peter Schmitt 00:05, 8 January 2010 (UTC)