%0 Journal Article %T Do the Two Operations Addition and Multiplication Commute with Each Other? %A Koji Nagata %A Tadao Nakamura %J Open Access Library Journal %V 2 %N 8 %P 1-4 %@ 2333-9721 %D 2015 %I Open Access Library %R 10.4236/oalib.1101803 %X We study about the metamathematics of Zermelo-Fraenkel set theory with the axiom of choice. We use the validity of Addition and Multiplication. We provide an example that the two operations Addition and Multiplication do not commute with each other. All analyses are performed in a finite set of natural numbers. %K Set Theory %K Formalism %U http://www.oalib.com/paper/3149246