Talk:Addition of natural numbers

I'd move this page to Addition of natural numbers, if agreed, for a clearer title. --G

OK, I'm not a real mathemetician, but I've never heard of a "hypothese". Is it a typo for "hypothesis"/"hypotheses", or just some specialist term I hadn't heard of? Don't want to go fixing it if it's right. -- John Owens 04:44 May 9, 2003 (UTC)

addition of odd numbers
I've never found an explanation about the sum of odd numbers, taking the first, second, third and so on. Let the odd numbers set be: {1, 3, 5, 7, 9, 11, 13, 15, ...}. Can someone tell me why the sum of n odd numbers, from the first, is always = n*n? For we have 1*1=1 (first number); 2*2=4 (first number [1] plus second number [3], [1+3=4]); 3*3=9 (1+3+5=9); 4*4=16 (1+3+5+7=16); 5*5=25 (1+3+5+7+9=25); 6*6=36 (1+3+5+7+9+11=36) and so on. So, if we have the sum of n successive odd numbers, starting by 1, than we'll have n to the square. I've never heard anything about such funny matter. Isn't it interesting? Will it be of some use? Time will tell.


 * Good observation, an explanation for the sum can be found at Arithmetic progression. --Salix alba (talk) 21:32, 13 May 2008 (UTC)

Proofs subpage, merge proposal
There have been numerous discussions about proofs subpages within the math project recently. There is not much support for keeping them, so over time some editors are working on merging the encyclopedic content. I am not sure that any of those facts needs to be proved in an encyclopedia article (which is not meant to be an axiomatic development). There are many good textbooks that will have these proofs and be a better resource to students.

Independent of that, I think that the content here could be merged into the main article on natural numbers. It seems odd to have a separate page devoted only to saying that addition of natural numbers is a commutative group operation. &mdash; Carl (CBM · talk) 00:06, 21 January 2010 (UTC)