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#92783 01/22/03 03:14 PM
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I've seen it as both CTN and COT.


k



#92784 01/22/03 04:05 PM
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I honestly thought ctn was a mistake. Every math book I've ever seen uses cot not to mention pretty much every programming language. In fact I thought it might have reached the stage of not being language-specific. emanuela, are the usual trig function abbreviations in Italian sin, cos, tan, sec, csc, cot? Anyone else with math and another language background care to comment?


#92785 01/22/03 07:02 PM
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http://www.bartleby.com/61/87/C0788700.html[
(Interestingly, I found a site that says that the maple programming language uses ctn and another that says it uses cot - perhaps both are correct and there's been a change. One Mathematica page explicitly says it's cot AND NOT ctn in that language.)

And people are actually using the notation, too http://web.mit.edu/wwmath/calculus/differentiation/trig.html3

http://www.mansd.org/memorial/mainsite/bb/other/nhoule/subdir/math.html

What I'm not sure of is how this varies - regional, perhaps, or maybe subject area (perhaps engineers are more likely to use ctn over cot), or perhaps even temporally (in the process of changing).

Similar notational deviance in a program language would be the use of the caret for exponentiation in some languages (fortran, pascal, vb, even quickbasic) vs double asterisk (perl, and the older versions of basic). [C, for example, doesn't even HAVE an exponentiation operator! It has the exp function, but no operator!]

Another notational oddity is that for the natural logarithm. Commonly ln or LN denoted natural log, while log denoted "log base 10" unless otherwise stated. Nowadays, I've seen class notes and handouts, etc, in which log denotes "log base e" unless otherwise stated.

On a slight, er, 'tangent,' one of the most curious terminological impasses I've encountered was the definition of a "Natural Number" which has changed over the years. When a woman first indicated in a usenet group that what she learned was that the naturals were the same as the integers I thought sure she was mistaken.

The whole thread is at http://makeashorterlink.com/?H32121033

k



#92786 01/22/03 07:32 PM
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the naturals were the same as the integers

I thought it was non-negative integers.


#92787 01/22/03 08:23 PM
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the naturals were the same as the integers



I thought it was non-negative integers.



Most of us (me included) learn a thing and think "well, that's the way it is." And we have a strong inclination (especially me) to think that opposing views are necessarily wrong.


What *I* learned:
N = Natural Numbers > 0
W = Whole Numbers >= 0
J = Integers = any non-fractional number
-- yet another thing ... sometimes they use the symbol I to mean integers
while my daughter is in pre-algebra in 7th grade and they use
J(n) to represent integers.

What this woman learned was that N = J. I was sure she was mistaken, but after spending a few hours in our company library I found a real math book that used her definition. (Which I meantion as the last post in that long thread of usenet posts I pointed to in my last message.)

Yet another weirdness which probably most awad readers are aware of, but don't think about very much. In 8th grade algebra, I learned that sqrt(-1) = i, but later, in engineering school, they used j for that.

It doesn't really matter how the terms are defined, so long as the terms are established early. Makes it difficult to interpret something when you come into it with no point of reference. That's obviously why they try to standardize some things.

k



#92788 01/22/03 08:29 PM
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I guess the only real contenders are the positive numbers (the orthodox view) and the non-negative numbers (the heretical view). One site I looked at suggested dropping the term completely; there were enough heretics running around that it was best just to say positive or non-negative or whatever you meant.


#92789 01/22/03 08:51 PM
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>I've never seen anything but cot for cotangent

i have :P -ctg


#92790 01/23/03 09:19 AM
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The way I was taught when I was learning to type was that it depended on the form of punctuation you were using.

If you were using 'closed punctuation' (considered old-fashioned)you would put a full stop after every abbreviation and initial, so...
Dr. A. N. Other

And when writing you would not leave a clear line between paragraphs, but would instead indent the first line of the paragraph by five spaces (1 tab stop).

This produced a fairly dense, cluttered page of type.

In 'open punctuation' you omitted full stops for abbreviations and initials...
Dr A N Other

and simply left a clear line between paragraphs instead of indenting the first line.

This produced a much cleaner page of type that was easier on the eye.


#92791 01/23/03 11:19 AM
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Interesting this topic should come up. I was recently reading a letter written by my grandmother. She was an appallingly lazy writer (I always wondered where that came from) and she abbreviated damned near every second word which made the letter rather hard to read. Frustratingly, she reduced names to R. and P. and what have you. Can't phone her and ask her now.

But, getting to the point, she put a full stop after every single one of those contractions and abbreviations. Looks pretty weird to moi, and I can be pretty pedantic!



- Pfranz

#92792 01/23/03 11:34 AM
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The i vs. j thing for imaginary numbers is usually an engineering/physics divide. I was told it was because engineers have a silly habit of using i for current and since you use imaginary numbers in decribing current and voltage in circuits, two different uses for the same letter would be confusing.

When I took real analysis (a hardcore math course in which we started by proving 2 > 1 and ended the year eight months later proving how to do calculus) we had natural numbers (N), that is, the "counting numbers" 0, 1, 2, 3,..., integers (...,-3, -2, -1, 0, 1, 2, 3...) (symbolized by Z - why has no one else mentioned Z?), rational numbers (Q) (any number that can be written as the quotient of two integers), irrational numbers (I, I think) (any number that CAN'T be written as the quotient of two integers), real numbers (R) (rational and irrational together), and complex numbers (C) which included all the others.

Note that for all of those the symbol is not just the letter but the funny letter with an extra bar which is completely unreproducible outside of TeX. (Having said that, maybe I'll make a little TeX file and post it somewhere so you can see what I mean. Give me an hour or two...I'm supposed to be working!)

Anyway, the naming is probably not so important as knowing what differentiates one group from another, what properties make one group different from the other.

emanuela could probably give us some definitive definitions on what's current in the "real math" world (rather than the bizarre world of the inconsistent drivel they teach kids in school - all you have to do is change provinces and the natural numbers could take on a whole different meaning - they should get their act together!).


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