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.

None?

There'll be a Beowulf Cluster of these along soon!

Ah, a little knowledge is a dangerous thing. What are these "+", "2", "=" and "4" things?

Over ZZ3 (integers modulo 3), 2+2=1.

When you learned to count (pre-school) you were actually learning what mathematicians call the successor function, and although the concept of zero was hard to understand, not only in Roman times, but even in the early Renaissance, current the symbol "2" is defined to be the successor of the successor of "0", and "+" is defined as moving an s() from one side to the other until a "0" has been reached on one side, at which point it can be dropped. So "2+2" = s(s(0)) + s(s(0)) = s(s(s(0))) + s(0) = s(s(s(s(0)))) + 0 = "4". IIRC, 0 can be defined as {} the empty set, s(s(x)) as {{x} u s(x)} or summat like that (not being rigorous, just lazy).

Anyway, a theorem of set theory may turn out to be used as an axiom for arithmetic, and that in turn used as an axiom (or given) for say calculus. But that doesn't make "2+2=4" a theorem at any sensible level, not even a lemma, but rather the definition of the symbols being used.

It turns out that many of the axioms of used in mathematics correspond to our natural understanding at an early level, and that in physics somewhat weird axioms can predict actual results, as in relativity and QM. When counting sheep jumping fences, integer arithmetic is enough. When counting cats in boxes, it isn't.

Hey! Which side are you on?

I've been trying to for years and then you mentioned it, you insensitive clod

All motherboards have em.

I scrolled down to see if there were any more relevant posts to reply to, but most of them also boasted about 80+ wpm.

I am by no means a touch typer, but I don't watch my keyboard either. So I correct a lot, and am about half your speed at best (say 50 wpm).

Still probably around 12 cps, but hitting Delete 3 times lowers the average, hehehe.

I still type faster than I can think, whether I am programming, translating, or writing for fun and pleasure. As the GP post said, any more is overkill for anything but data entry or transcribing.

As it happens, I didn't make many mistakes in the previous para, but I can regularly type stuff like: To be oare nto teo be, thatr ais the quzesition.

Thing is, when I'm typing text (using 9 fingers, not the right pinky for some reason, although I do sometimes use my left hand for control (thumb to C for copy, for example), I am aware of my mistakes and often want to change for other reasons anyway. And when programming, I want to type two or three letters and then code-complete.

You are forgetting the masses of seriously shitty coders out there who pump out 2000 "lines" per day, 250 days per year, who can get there in just 2 years.

I say 2000 lines because I can "create" that many in 8 hours no problem - it is only 4 lines per minute and I type at roughly 40 wpm when not thinking that much but still being aware of what I'm doing. But agreed, no way can a competent programmer do that every day!

My ThinkPad is dead you insensitive clod.

British mathematicians (from primary school to professor) place the decimal point not at the base, but half way up, at the same level as the minus sign, the space between the lines of an equal sign, or the intersection of the small "x" used as a multiplication sign.

This seriously confused an Italian boy who joined my school at age 14 and eventually was the other person from my year to go to Cambridge.

Unfortunately, despite his intelligence when he was first tested to see what group he should be in, he mistook the dot for a multiplication symbol. He'd been to American schools a lot, since his father was a diplomat. So he answered such simple questions as what is 1.2 + 3.4 (which should be 4.6) as 14 (1x2 + 3x4).

At least the GP understands that confusion is the issue. He is not 100% correct, but it isn't nonsense either.

Don't forget that not only written and spoken are important, but that the limitations of the ASCII/ANSI character set(s) mean that we use "full stops" rather than "points", and similarly combine multiplication into the asterisk.

That isn't very interesting, since it is the x86 (not the maths coprocessor) which has opcodes such as AAA and (see http://en.wikipedia.org/wiki/Intel_BCD_opcodes). The accuracy is the same, the performance of arithmetic operations is worse, but the important advantage of BCD on old architectures - including even the 4.77 MHz 8088 - is that they only had at best 16-bit registers, so the most you could represent unsigned was $655.35 (more than enough for anybody). Allowing a packed byte for the cents, and another for ones and tens, etc, may not have been the computationally most efficient, but without an '87, it was better than strings!