Re: [Phys-l] Carmichael numbers agai

["Folkerts, Timothy J" <FolkertsT@bartonccc.edu>]

> Well, not 'just like', because the above statement is not 
> quite true.  Remember that 2 is a prime number, and 2 is not odd.

:-)

I guess I wasn't quite thinking clearly!   You are correct, but
hopefully people get the idea.   I picked a weak example to try to
highlight the differences between: 
* If A, then B
* If B, then A
* If and only if A, then B

Tim F
-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of David
Bowman
Sent: Monday, May 21, 2007 12:09 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Carmichael numbers agai

Regarding Tim F's analogy,

> I don't think the original statement was ever meant to be a definition.
> It was a necessary but not sufficient condition.
>
> *All Carmichael numbers are the product of 3 or more primes, but not
all
> products of three or more primes are Carmichael numbers
>
> Just like
>
> * All primes are odd, but not all odd numbers are prime.
 
Well, not 'just like', because the above statement is not quite true.
Remember that 2 is a prime number, and 2 is not odd.
 
David Bowman
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