Hi John,

Le 18-août-06, à 03:03, <[EMAIL PROTECTED]> a écrit :

> Why has 6 'divisors'? because my math teacher said so?


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 
about.
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,

Bruno



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


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