Bruno,
           I'm terribly sorry to disappoint you and ashamed to admit that I'm 
"throwing in the towel". This is an idiom used in professional boxing; when a 
coach decides that his fighter can't take anymore punishment, he ends the fight 
by throwing a towel into the ring. I simply don't have the sort of mind that 
takes to juggling letters, numbers and symbols in increasingly fine-grained, 
complex arrangements. I think that in any endeavor, when we struggle towards a 
goal, there should be some satisfaction...some sense of accomplishment...in 
each step along the way. But in this quest, I find each step to be difficult 
and unrewarding in and of itself. Sometimes the goal is so compelling that we 
force ourselves to overcome huge impediments to reach it; but in this case, I 
already know what the goal is, and I am only motivated by the desire to 
understand how it is proven. Well, I must be content to leave verification of 
the proof to people who are far better able than I to follow its intricacies. I 
trust they have checked it accurately and will point out inconsistencies in 
this open forum if such exist. Meanwhile, I'm happy to take it on faith. I 
shall certainly continue to lurk here gleaning what I can from the 
philosophical debates whose endless probing of the foundations of existence is 
a source of constant fascination. Best,
                                                                                
                                                                                
      marty a.








           
----- Original Message ----- 
From: "Bruno Marchal" <marc...@ulb.ac.be>
To: <everything-list@googlegroups.com>
Sent: Friday, August 21, 2009 3:47 AM
Subject: Re: The seven step series


> 
> 
> On 21 Aug 2009, at 01:24, meekerdb @dslextreme.com wrote:
> 
>>
>> On Thu, Aug 20, 2009 at 12:32 PM, Bruno Marchal<marc...@ulb.ac.be>  
>> wrote:
>>>
>>>
>>> Hi,
>>>
>>> I give the solution of the first of the last exercises.
>> ...
>>> This motivates the definition of the following function from N to N,
>>> called factorial.
>>> factorial(0) = 1, and factorial(n) = n*(n-1)*(n-2)*(n-3) * ... *1, if
>>> is n is different from 0.
>>>
>>> Note this: if n is different from 0, for each n we have that  
>>> fact(n) =
>>> n*fact(n).
>>
>> Of course you meant fact(n)=n*fact(n-1).
> 
> 
> Yes, indeed.
> 
> Note that later we will see stronger form of recursion, but here it is  
> just a "typo" mistake.
> 
> Bruno
> 
> 
> http://iridia.ulb.ac.be/~marchal/
> 
> 
> 
> 
> >
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