## Comment Re:It's not the math ... (Score 1) 583

Oh dear, you actually do need a refresher course in mathematics.

What do you call an abelian group with an associative, distributive secondary operator and the power to corrupt mortals?

Answer here: http://www.irregularwebcomic.net/470.html

Apples and oranges are age 5 concepts of counting, at which point children aren't necessarily learning even to subtract yet. As a child I lived at #17, so #13 was two doors to the left, and #21 was two doors to the right. They were two doors away from my house, and from each other they were four doors! But my house was no doors from my house, it was (in more formal mathematical terms) O, the Origin, for me.

Next thing you will be telling me that Quaternions are a purely mathematical construct, with no physical analogue. Oh wait, how about Spacetime, you know, the natural universe we live in?

Now, defining Zero to be the equivalent of the empty set {} and then using the Peano axioms, THAT is a mathematical construct which can help us (mathematicians) to be rigorous (at least until Kurt F.ing Goedel comes along) without a direct physical analogue.

What confused you in your previous post is that the Romans had a perfectly good CONCEPT of zero (nullus) but lacked the notation for it, because they were (in CS terms) overloading their alphabet to do numbers too. Just as hexadecimal notitation does, feed face?

The reason that calculus is so common (not that I did it in my CS diploma, but then I have an M.A. in natural philosophy) a requirement is that Euler's formula brings together many of the (non-discrete) mathematical topics. I'm not sure to what degree (ha!) multiple differentiation (let alone integration) is relevant to a CS student, but a sound mathetical grounding is most certainly to be expected, just as biology and chemistry are to medical students, language to law and arts student, and ouija board usage to economists.

Furthermore, in a liberal (arts/science) degree, if you choose to be a science major of any kind, it would make sense that there is some sort of core curriculum which you are expected to be aware of at least, and where say a medical student might get away with slightly less on the maths front, I'd certainly hope they'd be able to understand that none/zero is one less than one in much the same way as one is one less than two.

Perhaps you are confused between ordinals and cardinals. It makes sense to say "I ate my first apple, then my second apple." It makes significantly less sense to then say "But before that, I ate my zeroth apple". If I have an apple, and you have an orange, then in the vector space of apples and oranges, I have (1, 0) and you have (0, 1). Those look remarkably different to me. However, if we both had 42 apples and 13 oranges, then the difference between our possessions would be NONE.