Why even ask a question like that? Everyone knows that , just like everyone knows that . Mathematicians would say that multiplication or addition of two numbers is *commutative*, meaning that you get the same answer regardless of the order in which you do the multiplication or addition.* * But what does that really mean? When we say , we literally mean “3, 4 times,” or 4 sets of 3 objects each, or objects. Likewise, when we say , we mean “4, 3 times,” or 3 sets of 4 objects each, or objects. Most people would think it’s obvious that , but it’s equivalent to saying that , which seems quite a bit less obvious. So how do we know it? Is the fact that multiplication is commutative just something we assume about numbers, or is there a way to prove it?