# Thread: Uses of the preposition "of" applied most often in math

1. ## Uses of the preposition "of" applied most often in math

I am looking for any reference articles on the uses of the preposition "of" that are applied most often in mathematics. I once read in the teacher's edition of Pre-algebra: An Accelerated Course by Dolciani that students should be taught, as early as possible, the many uses of the preposition "of" in mathematics, but I have been unable to find anything on this particular question/topic. Could you please help me find something? (books, articles, etc.)

Please note: The primary tag for this thread is a REFERENCE-REQUEST. Reference-requests are for questions that the poster wants to seek for references (books, articles, etc.) in a subject.

So far the only references that I have found can be viewed at these URL's :
Professor Richard Milton Martin

Pragmatics, truth, and language - Google Books

Professor Pat Byrd

Of

Unfortunately, they are at opposite ends of the spectrum with reference to my question about the uses of "of" most often applied in mathematics.

Yours respectfully.
Pragmatics, truth, and language - Google Books

2. Well, I don't know about reference works, but the two uses I see most often are to indicate either multiplication, or function application.

Example of multiplication: Ten is what percent of forty? Translation: 10 = WP * 40, with solution WP = 25%.

Example of function application: sine of x, written sin(x).

That's admittedly off the top of my head. I suppose, in more advanced mathematics, you also have "of" meaning the application of an operator, like this: the derivative of f(x), or the integral of f(x), etc.

3. I remember being taught in primary school 60 years ago that "of" always means "times" in arithmetic: "two-thirds of 12" means $\displaystyle \frac23\times12$; "a quarter of an hour" is $\displaystyle \frac14\times60$ minutes.

Apart from that, I think that "of" usually has the same functions in mathematics that it has in ordinary language, to indicate possession or membership.