- The point is we have two words which mean exactly the same thing. I'm not

going to force anyway to accept my usage, but I can't see any harm in the

splitting of the definitions. Helps me out anyway.

Jon Perry

perry@...

http://www.users.globalnet.co.uk/~perry

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-----Original Message-----

From: Jud McCranie [mailto:jud.mccranie@...]

Sent: 31 October 2001 22:43

To: Jon Perry

Cc: primenumbers@yahoogroups.com

Subject: RE: factor distinguished from divisor ; was [PrimeNumbers]

Prime formula

At 07:52 PM 10/31/2001 +0000, Jon Perry wrote:>As they are vague, I think I'll stick with my factor is a prime, and

divisor

>is the product of one or more primes.

This website says they are the same.

http://www.utm.edu/research/primes/glossary/Divisor.html

In fact the entry for "factor" links to "divisor".

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Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/ - I'm not sure why certain people have trouble with this concept. I

really don't have an explanation for that. The only thing I can think

of is ring theory, ideal theory.

Here is an analogy.

Take a typical flawed definition of perfect:

A perfect is the sum of all its factors.

Actually this isn't too typical.

Authors often account for one of these factors 8->

positive

proper

Let's account for both:

A perfect is the sum of its positive factors, except itself.

Take 28 as an example.

The "factors" are 1, 2, 4, 7 and 14.

Since factors imply a product, this product would be 784.

It's really hard to imagine how to obtain 28 as a product from that set

(though I confess 29 would be even more of a challenge 8-> ).

What would the rationale for selection be?

Now, by analogy, would you apply the same standard to divisor that you

apply to factor?

Suppose the set { 31 , 32 } is under discussion. Would you say the

elements of this set are integers? Would you say the elements of this

set are divisors? Of course, it _is_ a fact that they are divisors, of

say, 4063232. So what? How is that relevant to anything worth saying

here? Unless something more is happening, this is a set of integers.

And, I would suggest, in the context above, { 1 , 2 , 4 , 7 , 14 } is a

set of divisors.

Simple (albeit incomplete) operational process for authors:

If all numbers in a set are real, call them real.

If all are algebraic, call them algebraic.

If all rational, call them rational.

If all integer, call them integer.

If all divisors of some number under consideration, call them

divisors.

If all are factors of some number under consideration, call them

factors.

If all are prime factors of some number under consideration, call them

prime factors.

You can stop short in this process; you won't be incorrect. But you

also may not be making the best use of your communication. But going

too far in this process is wrong, misleading, confusing.

These distinctions are valuable and they should be preserved.

It's a simple matter of clarity.

> Doesn't the fact that 28 is a divisor/factor of

Surely, yes, even 784\28. 8->

> 784 imply that 784/28 is also a divisor/factor?

> > > a factor can be equal to zero

My remark, two messages ago, was so restricted. By me. I didn't want

> > Again, as you know, not in Z+.

> Who did decide this restriction?

to wander off into ring theory, and in a mailing list named

primenumbers, the naturals seemed like a natural 8-> set. Others are

welcome to take up Z, Q, etc.

> Of course, 'to be a factor' and 'to be a divisor' are not intrinsic

Yes, good.

> properties of a number, they obviously depend on the context.

> Personally, I regard these words as the will of their author to give

> me more information (even fuzzy) about the origin, the destination,

> the possible use, whatever, concerning a number in a given context.

> the meaning of a word is neither definitive nor the same for

Not all the money you receive is genuine. That doesn't mean the

> everybody.

counterfeit is less bad.

If we can agree on the meaning of terms such as "greater", "product",

"distinct", "odd", "set", "positive" (as distinguished from

"non-negative"), "integer", "monotonic", "prime", "factor", "twin

primes", "circle", "phi", then we can communicate more clearly and more

easily.

> Trying to legislate on that is not far from a pure waste of time.

Short of legislation is a process called standardization. It can be

formal or de facto. It's more of a good thing than a bad thing.

Cheers.

Walter Nissen