Originally Posted By: Bill S.

Would I be spoiling an academic discussion if I were to ask what, in the real world (whatever that is), is the distinction between: a banana and a banana^2?


Part of the beauty of algebra - which is a foundation of all higher, analytic math (geometry, trig, analytic geometry, calculus, probability, statistics, differential equations, linear algebra, numerical analysis, etc.) - is that interim results don't need to have a physical interpretation.

What's important is that what you have on both sides of an equal sign are actually equal - and that can't happen if the dimensions are inconsistent.