----- Original Message -----
From: "Bruno Marchal" <[EMAIL PROTECTED]>
Sent: Friday, August 18, 2006 11:23 AM
Subject: Re: ROADMAP (well, not yet really...
Le 18-août-06, à 03:03, <[EMAIL PROTECTED]> a écrit :
> Why has 6 'divisors'? because my math teacher said so?
>Now I know you are joking. I know that you know that six has divisors.
It follows from the elementary definitions...<
Yes, I was. Not now: WHO supplied those "elementary definitions"?
Surely a math teacher or the ancestor of such. Not even Gauss was born with
the knowledge that 6/2=3.
Just as those "axioms" Stathis finds 'explanatory' stem from necessity to
hold a "theory" valid. Another view of the world would require different
Brent wrote about the crows who "counted" to 5, with some uncertainty even
higher and concluded that 'numbers exist in nature' - I did not examine what
the crows think, whether it was just a waiting period until their memory
expired, and the wise experimentors assigned it to 'counting' - all in their
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.
(If 1 is a divisor - meaning 1x6 = 6 then 6 is also one: 6x1 = 6). An
exclusion of '1' would give a sum of 5 - Unless you want to exclude the
'number itself' from the "sum" - in which case the sum of "1" would be zero
(excluded the 1).
NOW I was joking.
I say to my students that in case they are saying a falsity (in math),
they will get a bad or a good note, depending on the way they will
defend the proposition. If they defend it by saying "because you say so
during the course", then they will get a *very* bad note, indeed!
Even, and I would say *especially* if it is true, that I have said that
falsity. Actually I teach like that, I make error all the time (mostly
intentionally but of course not always). It works. Students eventually
understand that they must understand math by themselves. Each year I
have student (about 20 years old) just realizing what math is all
Now I know you are joking. I know that you know that six has divisors.
It follows from the elementary definitions. And I will not repeat them,
because that would be sort of an insult (of course a number is
"perfect" if it is equal to the sum of its proper divisors ... by
definition. Why using the word "perfect"? Pythagorean superstition or
folklore, but mathematicians are not sanguine about words and
representations. In the lobian interview all natural numbers are
represented by strings like 0, s(0), s(s(0)), s(s(s(0))), etc.
Best regards, bon week-end,
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