About Joe's article multiplication is not commutative

[John P]

I think the title of Joe's article is a bit provocative but not precise because it is missing some kid of qualifier. "Multiplication is not commutative", it is not commutative in general or on the Moon or maybe on the Mars. In general things stay the same and multiplication is commutative but on calculators or on computers real and irrational numbers are represented as approximations so we should not be talking about not commutative multiplication but about error the floating point multiplication introduces on HP Prime or on any other computing device.