Why Are There Different Notations for Scientific Symbols?

[Elbobo]

Couldn't find my answer on Google...

Often, I hear some character like a₀ pronounced ay-ZEE-ro, ay sub-ZEE-ro, or ay-NOT. Purely out of curiosity, where does this last name for a₀ come from? Origin? Actual spelling?

Second, I've seen the symbol for velocity written as both the normal letter v (as the Romantic languages are accustomed to), and the Greek letter $$\nu$$ (nu). Which one is technically correct in the eyes of the professional science community (e.g., in journals, publications, reports, etc.)?

EDIT: Oh and last, DERIVATIVES. I've seen them written and typed dy/dx for example, but I've also seen cases where the d is a bit more stylized and somewhat resembles a backward "6." That's not any Greek letter that I know. Any clarification on usage there?

Sorry if these seem like frivolous questions, but I like knowing the proper way of things :) Semantics, pedantic, yeah yeah, I'm one of those.

 

[CompuChip]

It does sound a lot like "not", as a non-native speaker it took me a while to figure it out as well (professors from all over the world pronouncing it in broken English did not help either). But it is actually "nought" :-)

For velocity, the letter v is correct, in my opinion. It stands for "velocitas", as far as I am concerned. (Interestingly, the letter c for the speed of light is of similar origin. I think it was coined by Einstein, who used it as an abbreviation of "celeritas" - which basically also means speed in Latin).

There is actually a difference between something like $$\frac{df}{dx}$$ and $$\frac{\partial f}{\partial x}$$. The $\partial$ symbol looks like a Greek letter perhaps, but it is actually not (it's just a stylised d, as you say). People usually pronounce it "dau" ("dow") or "partial".
I don't know if you have seen any multi-variable calculus yet, but suppose you have a function f(x, y) = x y. Of course, it may be possible that y is itself a function of x (for example, in the simplest case y = x). In that case, the "partial" derivative treats the y as a constant, while the "total" derivative does not. So
$$\frac{\partial f}{\partial x} = y$$
while to the d/dx operator f(x, y) looks like x², and
$$\frac{df}{dx} = 2 x$$.
You can easily imagine an application in physics, where you have something depending on position and time explicitly, e.g.
f(x, t) = e^x + t².
However, usually the position x also varies with time, so actually x = x(t) is a function of t. Then it begins to matter which of the two you use, since e^x is just a constant, vanishing under the partial derivative operator, in one case, while it actually gives a non-trivial contribution of x'(t) e^x(t) in the other.

 

[jtbell]

ay-NOT

That's "a-naught". Look up the word "naught". It's hardly ever used in American English, but I understand the British use it more often.

(added: hah, I guess we Yanks use it more than I thought. The three usage examples shown in Google's dictionary are all quotes from Americans.)

 

[CompuChip]

By the way, I have the impression that some people actually write a little circle, more like the letter o than the figure 0.
In fact, I have even seen it used in typed documents: $$a_o$$ or $$a_{\mathrm{o}}$$ instead of $$a_0$$ (probably because the author(s) thought the 0 was too large or did not resemble the way they wrote it).

 

[jtbell]

Second, I've seen the symbol for velocity written as both the normal letter v (as the Romantic languages are accustomed to), and the Greek letter $$\nu$$ (nu).

That thing that looks like a Greek $\nu$ is actually an italic v ($v$). The difference is rather visible in LaTeX on my browser. In some books, they look a lot more alike.