Mathematical uses of the preposition "of"

skullpatrol

Dear Professors,

I am looking for any articles on the uses of the preposition "of" in mathematics. I once read in a teacher's edition of a pre-algebra textbook that suggested 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 anyone please try to help me find something? Or better still could anyone give me an outline of these uses?

Yours respectfully, Rob

Mark44

I'm not sure 'the uses of the preposition "of" in mathematics' is worthy of an entire article, but who knows?

Aside from the ordinary meaning to indicate membership, the only sense of "of" I can think of that might be interesting here is when it means "multiplied by," when we're talking about a fractional part of something; e.g., "1/2 of 12."

symbolipoint

"Of" is a preposition and its meaning depends on the conventions for the human language which applies it. In English, "of" will often mean "multiplication", but the reader or writer needs to understand the worded description of the exercise or problem description to be able to properly understand what "of" means. Nine eggs of a packaged dozen, would mean possibly, 9 divided by 12, therefore, meaning three fourths, or 75% or nine twelfths. Seventy five percent of twelve would mean (3/4) multiplied by 12, and therefore mean 9.

skullpatrol

To whom it may concern,

May I suggest the topic of this thread be modified to better convey my intent:

Uses of "of" applied most often in math and why?

In my humble opinion, the answer to why mathematicians apply certain uses of "of" more often
can give us a much deeper understanding into the nature of the art.

skullpatrol

May I suggest the topic of this thread be modified to better convey my intent:

Uses of "of" applied most often in math and why?

In my humble opinion, the answer to why mathematicians apply certain uses of "of" more often
can give us a much deeper understanding into the nature of the art.

#1) the cause, effect, origin, reason, result of;

#2) the correlative, counterpart, match, opposite, original of;

#3) a copy, derivative, image, likeness of;

#4) the square, cube, logarithm, tangent, differential, or other mathematical function of.

skullpatrol

Please note: I am NOT saying that the preposition "of" has a "unique-mathematical-meaning" when used by mathematicians. What I am intending to convey is that of all the general usages that can be found at dictionary.com for "of", mathematicians CHOOSE to use a limited subset of them i.e. examining the usages of "of" applied most often in math and asking WHY did they choose this specific subset? Is, in my opinion, a question worth trying to answer because it will provide us with a valuable insight into the nature of the art.


If on the other hand you find it useless that I am trying to explain to others the beauty of mathematics through its choice of vocabulary and why that choice was made as demonstrated by any future comments about counting occurrences of "of" in mathematical writing, being unduly obsessed, or even categorizing what I am trying to do as the subject of a "crank."

May I describe mathematics as the art of creating images and establishing relationships, is it not so that the "material" of this activity are thoughts? And since words convey those thoughts we must "measure" our choice of words carefully for the sake of lucidity.

The sheer number of occurrences of "of" in academic writing and in mathematical writing in particular, justifies, in my opinion, at least an honest attempt at "looking for any articles on the uses of the preposition "of"...I have been unable to find anything on this particular question/topic. Could you please help me find something?"

PLEASE NOTE THE BOTTOM LINE OF THIS THREAD IS A REFERENCE-REQUEST

Yours respectfully.

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skullpatrol

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

http://books.google.com/books?id=L0P...page&q&f=false

Professor Pat Byrd

http://www2.gsu.edu/~eslhpb/grammar/lecture_11/of.html

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.