Thanks for telling Marty.
It is a pity you stop just before Cantor Theorem, but it could ask for
some work if your math disposition have been dormant for a too long
I am sure you could come by, because what will follow will be a
recurrent use of the same idea.
The difficulty, for many, is to understand what is a mathematical
computation, but to explain this we have to explain what are the
mathematical objects which will computed and be computed.
Sets of numbers and functions from numbers to numbers are those things
which will be either computable or not computable.
Up to now, I am only introducing vocabulary, so that we can avoid
future misunderstanding. Numbers, sets, functions are common in "exact
science", but rarely well known ...
I will soon explain Cantor theorem. And soon after should the
"mathematical discovery of the (mathematical) universal machine" appear.
I have to explain a minimal amount of theoretical computer science to
give a precise sense to the comp supervenience thesis.
I like to summarize 20th century computer science by its two main
'discoveries', really two creative bombs, the universal machine, and
the other universal machine. The universal machine, and the quantum
universal machine. I put 'discoveries' in quote because strictly
speaking they are thesis or hypothesis.
Take a look on what follows because it happen that some beginners
understand math the day they understand the first non trivial result,
but take it easy any way. It is a pleasure to share interest wherever
we come from, and I appreciate your open mind,
On 21 Aug 2009, at 16:22, m.a. wrote:
> 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,
> ----- Original Message -----
> From: "Bruno Marchal" <marc...@ulb.ac.be>
> To: <email@example.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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