----- Original Message -----
From: "Bruno Marchal" <[EMAIL PROTECTED]>
To: <everything-list@googlegroups.com>
Sent: Tuesday, August 22, 2006 6:04 AM
Subject: Re: ROADMAP (well, not yet really...
(See below)
========================
Teach! -
 I have a difference against your mathematical definition! (ha ha)

I thought if  '1' is a proper divisor of a number, then the number itself is
also.
Upon your post I looked up Wikipedia: "divisor" (nice page) and copied from
it:
*
"For example, 7 is a divisor of 42 because 42/7 = 6. We also say 42 is
divisible by 7 or 42 is a multiple of 7 or 7 divides 42 and we usually write
7 | 42. For example, the positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21,
42.
*
I don't think 42 is so different from 6. If you abandon "the number itself",
you MUST abandon the "1" as well and in that case 6, indeed nothing is a
perfect number.
I really had that suspicion that 'numbers' are not so perfect!
(metaphorically).

(I have an idea why it is important to leave out "the number proper": if '1'
and the 'number' are included, there would be NO PRIME NUMBER at all. Would
be a shame! Sorry for 37 indeed.
 Of course the definition of 'prime number' excludes 'the number itself and
'1' - which, however, is not binding to the 'definition' of a divisor.)

Pupil John
======================================

Le 19-août-06, à 21:13, <[EMAIL PROTECTED]> (John M.) a écrit :

> BTW I have a problem with the "perfect" 6:
> ITS DIVISORS are 1,2,3,6, the sum of which is 12, not 6 and it looks
> that
> there is NO other perfect number in this sense either.

I have define a number to be perfect when it is equal to the sum of its
proper divisor. Six is not a proper divisor of six.

Bruno

http://iridia.ulb.ac.be/~marchal/





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