Anyone knows how to enter ’ on us mac keyboard?
(right single quote)
Found it on alt+e.
Any strong opinions on whether to write i.e. with or without italics?
also with or without a comma
without?
Gold!
The derivative is the limit of (small_change_in_y / small_change_in_x) as these changes get smaller (assuming there is such a limit).
Each of these “change” values is the difference (subtraction) of an initial value from a terminal value:
small_change_in_y = y_end - y_start
small_change_in_x = x_end - x_startSince y is a function of x, we can say:
y_start = f(x_start)
y_end = f(x_end)Given all this information, (small_change_in_y / small_change_in_x) is often written out as ((f(x_start + small_change_in_x) - f(x_start)) / small_change_in_x). Anyhow, I think the subtractions are were the “differences” come in.
The (modern) usage of the words is: differential quotient = f’(x0) (the value at a point x0) derivative = f’(x) (the function from points to differential quotients)
On the topic of “i.e.” I always write without the comma, and in plain text rather than italics. That said, I don’t make any claim that this is correct, I probably just ended up doing things that way out of laziness as much as anything.
In case anyone wants a Christmas-time puzzle: https://www.gchq.gov.uk/news/christmas-card-2020
@rokitna, that makes a lot of sense. I would love to look up a reference with historical evidence for the word usage. If any of you happen to know one, it’ll be great!
Hm, I don’t know of anything that goes into well-sourced detail on why these particular things are called what they are. I’d be interested to see something like that too. I only know enough to explain why I thought it made sense, and this means I could easily be on the wrong track.
Not a strong opinion, but I would keep the italics because it is an expression from a foreign language. In fact, I’m not very food of the abbreviation “i.e.” Abbreviations are useful when really everyone knows what it means. But it turns out a lot people don’t master these Latin expressions. I tend to write “et cetera”, for instance, and the last time I did an editor rewrote it to “etc.” It boils down to taste. So make sure to do something you like best. :slightly_smiling_face:
I would bet 100 USD that you’re right. :slightly_smiling_face: For the record, another word that I would like to understand better is logarithm. Another one is root. I believe “root” might have come from “raiz”, which was a perhaps mistranslation of Greek’s “radix”, which must mean “base”. Now “root” is some kind of base, right? Plants do depend on roots to keep them firm on the ground. I only trust the etymology of “algorithm” because I read it from Knuth.