# Talk:263: Certainty

This was done 6 years later by Fox News. 72.70.180.234 10:44, 31 May 2013 (UTC)

It's easy to politicize that. Abelians versus non-Abelians ;) Not all vector spaces will likely share the property seen there.67.204.136.58 23:34, 15 August 2013 (UTC)

If you flip ab + ac around, you end up with ac + ab which looks a lot like ACAB and that can get political very fast. 94.76.233.42 (talk) *(please sign your comments with ~~~~)*

Abelian means that ab = ba, but this distributive law is different. Both the distributive property and the Abelian property are assumed properties of numbers, i.e., accepted as true and used to prove more complicated properties. Non-Abelian examples of objects that "look" like numbers are not too hard to construct. One interesting example is where "a" abd "b" are rotating a book clockwise 90 degrees (a) and rotating the book forward 90 degrees (b). Start with the book facing you for reading and first do "a", then "b", which is written "ab". The result has the front of the book facing up. Now do "b" first, then "a", to get "ba". Now the binding of the book is facing up and the front of the book is facing to the right. So, "ab" is not "ba". The best I can think of for the distributive type of thing is for everything to make sense, except b+c is something for which multiplying by "a" is undefined.--DrMath 09:07, 22 November 2013 (UTC)

But what about cryptography? A mathematical topic, and hardly apolitical nowadays. However, I appreciate and enjoy Randall's sentiment about the purity of mathematics. 108.162.219.223 20:23, 17 January 2014 (UTC)