The noncommutativity of addition

You know that thing I said earlier, about there not being any "two numbers, a and b, so that a+b≠b+a"?

Well, scratch that! I just found two numbers for which this is, in fact, the case, namely 176 and 12.3. See? 176+12.3 equals 188.3, whereas 12.3+176, on the other hand, equals...

Okay, back to the drawing table.