forum. I don't
dare to put my username on this list ;-)
Bruno
>
> - Original Message -
> From: Bruno Marchal
> To: everything-list@googlegroups.com
> Sent: Wednesday, December 09, 2009 2:25 PM
> Subject: Re: The seven step series (december 2009)
>
>
> On 09 Dec
-
From: Bruno Marchal
To: everything-list@googlegroups.com
Sent: Wednesday, December 09, 2009 2:25 PM
Subject: Re: The seven step series (december 2009)
On 09 Dec 2009, at 01:42, m.a. wrote:
Bruno,
This is a stupid question but I'm hoping it contains the k
On 09 Dec 2009, at 01:42, m.a. wrote:
> Bruno,
>This is a stupid question but I'm hoping it contains the
> kernel of an idea. Since logic is based on a few common definitions,
> do you really need all these complicated steps and permutations to
> prove a theory? Why can't you sh
ar, simple, logical statements?
marty a.
- Original Message -
From: Bruno Marchal
To: everything-list List
Sent: Monday, December 07, 2009 1:12 PM
Subject: Re: The seven step series (december 2009)
Hi,
We may be at a cross of the "se
Hi,
We may be at a cross of the "seventh step" and "Why I am I?" thread.
Chose your favorite universal system.
Like LISP, FORTRAN, the combinators, the diophantine equations, etc.
Enumerate in lexicographical order the expressions corresponding to
the algorithms of the partial computable funct
On 16 Nov 2009, at 17:45, Brent Meeker wrote:
> Bruno Marchal wrote:
>>
>> On 11 Nov 2009, at 19:52, Brent Meeker wrote:
>>
>>>
>>> But how is the "first person point of view" defined? Can this
>>> theory
>>> tell me how many persons exist at a given time?
>>
>>
>> I come back on this. The que
Bruno Marchal wrote:
>
> On 11 Nov 2009, at 19:52, Brent Meeker wrote:
>
>>
>> But how is the "first person point of view" defined? Can this theory
>> tell me how many persons exist at a given time?
>
>
> I come back on this. The question "how many persons?" is a question
> which remains very
On 11 Nov 2009, at 19:52, Brent Meeker wrote:
>
> But how is the "first person point of view" defined? Can this theory
> tell me how many persons exist at a given time?
I come back on this. The question "how many persons?" is a question
which remains very hard in the mechanist theory.
To an
On 11 Nov 2009, at 19:52, Brent Meeker wrote:
>
> Bruno Marchal wrote:
>>
>> On 10 Nov 2009, at 19:29, Brent Meeker wrote:
>>
>>
>>> But this seems like creating a problem where none existed. The
>>> factorial is a certain function, the brain performs a certain
>>> function.
>>> Now you
Bruno Marchal wrote:
>
> On 10 Nov 2009, at 19:29, Brent Meeker wrote:
>
>
>>>
>> But this seems like creating a problem where none existed. The
>> factorial is a certain function, the brain performs a certain function.
>> Now you say we will formalize the concept of function in order to study
Rex Allen wrote:
> On Tue, Nov 10, 2009 at 1:29 PM, Brent Meeker
>> That's why I say I take it as an ansatz - "Let's consider
>> all possible computations and see if we can pick out physics and the
>> brain and consciousness from them."
>>
>
> I would think that it's pretty much a given t
On 11 Nov 2009, at 08:48, Rex Allen wrote:
>
> On Tue, Nov 10, 2009 at 1:29 PM, Brent Meeker
> >
>> That's why I say I take it as an ansatz - "Let's consider
>> all possible computations and see if we can pick out physics and the
>> brain and consciousness from them."
>
> I would think that it
On 10 Nov 2009, at 19:29, Brent Meeker wrote:
>>
> But this seems like creating a problem where none existed. The
> factorial is a certain function, the brain performs a certain
> function.
> Now you say we will formalize the concept of function in order to
> study
> what the brain does and
On Tue, Nov 10, 2009 at 1:29 PM, Brent Meeker
> That's why I say I take it as an ansatz - "Let's consider
> all possible computations and see if we can pick out physics and the
> brain and consciousness from them."
I would think that it's pretty much a given that out of all possible
computations
Bruno Marchal wrote:
>
> On 09 Nov 2009, at 20:43, Brent Meeker wrote:
>
>>
>> Bruno Marchal wrote:
>>>
>>> Hi,
>>>
>>> Let us come back on the "seven step" thread.
>>>
>>> Let me recall the initial motivation. The movie graph argument (cf the
>>> MGA thread) shows that it is senseless to attach c
Bruno Marchal wrote:
>
> Hi,
>
> Let us come back on the "seven step" thread.
>
> Let me recall the initial motivation. The movie graph argument (cf the
> MGA thread) shows that it is senseless to attach consciousness to the
> physical activity of a brain or a computer.
>
> If we keep the comput
Hi,
Let us come back on the "seven step" thread.
Let me recall the initial motivation. The movie graph argument (cf the
MGA thread) shows that it is senseless to attach consciousness to the
physical activity of a brain or a computer.
If we keep the computational thesis for the cognitive pro
Hi John, hi Marty,
On 10 Oct 2009, at 21:47, John Mikes wrote:
> Bruno, we had similar puzzles in middle school in the 30s.
> The barber could not shave himself because he shaved only those who
> did not shave themselves (and shaved all). So for (Q #1) in the 1st
> vriant
> she(?) was a femal
- Original Message -
From: John Mikes
To: everything-list@googlegroups.com
Sent: Saturday, October 10, 2009 3:47 PM
Subject: Re: The seven step series
Bruno, we had similar puzzles in middle school in the 30s.
The barber could not shave himself because he shav
essage -
From: John Mikes
To: everything-list@googlegroups.com
Sent: Saturday, October 10, 2009 3:47 PM
Subject: Re: The seven step series
Bruno, we had similar puzzles in middle school in the 30s.
The barber could not shave himself because he shaved only those who did not
s
Bruno, we had similar puzzles in middle school in the 30s.
The barber could not shave himself because he shaved only those who did not
shave themselves (and shaved all). So for (Q #1) in the 1st vriant
*she(?)* was a female, unless *he(?)* was a beardless male
(and the 'all' refers to only the *be
Hi,
I am so buzy that I have not the time to give long explanations, so I
give here a short exercise and a subject of reflexion instead.
Exercise:
There is Tyrannic country where by law it was forbidden for any man to
have a beard.
And there is village, in that country, and it is said that
Hi,
I sum up the definition and results seen so far.
N = {0, 1, 2, ...}, the set of natural numbers (also called positive
integers).
N^N = {f such that f is a function from N to N} = the set of functions
from N to N.
Universal language: a language in which we can describe formally how
to
On 18 Sep 2009, at 17:00, I wrote:
> On the set N^N of all functions from N to N, Cantor diagonal shows
> that N^N is non enumerable.
> On the set N-N-comp, the diagonal shows that N^N-comp, although
> enumerable is non computably enumerable.
>
> OK? take the time to swallow this, and ask
I give the answer.
On 17 Sep 2009, at 16:27, Bruno Marchal wrote:
>
> On 16 Sep 2009, at 18:12, Bruno Marchal wrote:
>
>
>>
>>
>> If it is OK, in the next post we begin to address the computability
>> issue. I give you an anticipative exercise or subject reflection.
>> This is a deep exercis
Yes, Bruno, it helps - however: I did not want to put you into any apology!
The list is a free communication among free spirits and controversy is part
of it.
What I 'read' in your reply still "sticks" within 'math' and my principal
point is: the image represented is STILL what a human mind MAY thi
On 17 Sep 2009, at 18:17, John Mikes wrote:
> Dear Bruno,
>
> it is not very convincing when you dissect my sentences and
> interject assuring remarks on statements to come later in the
> sentence, negating such remarks in advance, on a different basis.
>
> I argued that - upon what you (an
Dear Bruno,
it is not very convincing when you dissect my sentences and interject
assuring remarks on statements to come later in the sentence, negating such
remarks in advance, on a different basis.
I argued that - upon what you (and the rest of the multimillion
mathematicians past and present)
On 16 Sep 2009, at 18:12, Bruno Marchal wrote:
>
>
> If it is OK, in the next post we begin to address the computability
> issue. I give you an anticipative exercise or subject reflection.
> This is a deep exercise. Its solution leads to the notion of
> universal function and universal num
Hi John,
On 17 Sep 2009, at 15:14, John Mikes wrote:
>
>
> You went out of your way and did not save efforts to prove how
> inadequate and wrong (y)our number system is. (ha ha).
Wrong ?
>
> Statement: if square-rooting is right (allegedly, and admittedly)
Well, it is certainly right if w
Bruno,
I loved your post on the square root of "2"!
(I also laughed at it, to stay at the puns).
You went out of your way and did not save efforts to prove how inadequate
and wrong (y)our number system is. (ha ha).
Statement: *if square-rooting is right* (allegedly, and admittedly) *then
THERE I
I give the solution.
On 15 Sep 2009, at 16:30, Bruno Marchal wrote:
> OK? Take your time to compare with the last post, and to understand
> what happens.
>
> Training exercise: prove, using that notation, that 2^N is non
> enumerable. Hint: use a slightly different g.
2^N is non enumerable.
Hi,
I will introduce notation for functions, and prove again Cantor
theorem, without making any diagram.
I will lazily write the diagram
>
> 0 => 34, 6, 678, 0, 6, 77, 8, 9, 39, 67009, ...
> 1 => 0, 677, 901, 1, 67, 8, 768765, 56, 9, 9, ...
> 2 => 1, 2, 4, 8, 16, 32, 64
On 09 Sep 2009, at 09:21, Bruno Marchal wrote:
> Next post: Cantor theorem(s). There is NO bijection between N and
> N^N. I will perhaps show that there is no bijection between N and
> {0, 1}^N. The proof can easily be adapted to show that there is no
> bijection between N and many sets.
>
Hi,
I want to add something.
I said recently to John that the excluded middle principle should be
seen as a tolerance-of-ignorance principle. Actually this will play an
important role later, and it justifies the "arithmetical realism":
what it is, and why it is important.
Let me illustrate
This is the last post before we proof Cantor theorem. It is an "antic
interlude". We are about 2000 years back in time.
The square root of 2.
It is a number x such that x^2 = 2. It is obviously smaller than 2 and
bigger than 1. OK? It cannot be a natural number. But could it be a
fraction?
m: "Bruno Marchal"
> To:
> Sent: Tuesday, September 08, 2009 4:43 AM
> Subject: Re: The seven step series
>
>
>>
>>
>> On 31 Aug 2009, at 19:31, Bruno Marchal wrote:
>>>
>>>
>>> Any question, any comment? I guess that I am too quic
ll be equally clear. Best
wishes,
marty a.
- Original Message -
From: "Bruno Marchal"
To:
Sent: Tuesday, September 08, 2009 4:43 AM
Subject: Re: The seven step se
On 31 Aug 2009, at 19:31, Bruno Marchal wrote:
>
> Next: I will do some antic mathematic, and prove the irrationality
> of the square root of two, for many reasons, including some thought
> about what is a proof. And then I will prove Cantor theorem. Then I
> will define what is a computabl
On 02 Sep 2009, at 17:16, Mirek Dobsicek wrote:
>
> Bruno Marchal wrote:
>> Ouh la la ... Mirek,
>>
>> You may be right, but I am not sure. You may verify if this was not
>> in
>> a intuitionist context. Without the excluded middle principle, you
>> may
>> have to use countable choice in som
Bruno Marchal wrote:
> Ouh la la ... Mirek,
>
> You may be right, but I am not sure. You may verify if this was not in
> a intuitionist context. Without the excluded middle principle, you may
> have to use countable choice in some situation where classical logic
> does not, but I am not sur
Ouh la la ... Mirek,
You may be right, but I am not sure. You may verify if this was not in
a intuitionist context. Without the excluded middle principle, you may
have to use countable choice in some situation where classical logic
does not, but I am not sure.
I know that in intuitionist ma
The reason why I am puzzled is that I was recently told that in order to
prove that
* the union of countably many countable sets is countable
one needs to use at least the Axiom of Countable Choice (+ ZF, of
course). The same is true in order to show that
* a set A is infinite if and only if th
Hi Mirek,
On 01 Sep 2009, at 12:25, Mirek Dobsicek wrote:
> I am puzzled by one thing. Is the Axiom of dependent choice (DC)
> assumed
> implicitly somewhere here or is it obvious that there is no need for
> it
> (so far)?
I don't see where I would have use it, and I don't think I will us
Hi Bruno,
I am puzzled by one thing. Is the Axiom of dependent choice (DC) assumed
implicitly somewhere here or is it obvious that there is no need for it
(so far)?
Thanks!
mirek
--~--~-~--~~~---~--~~
You received this message because you are subscribed to the
I give the solution to the last exercises.
On 26 Aug 2009, at 19:06, Bruno Marchal wrote:
>
> Hi,
>
> I sum up, a little bit, and then I go quickly, just to provide some
> motivation for the sequel.
>
> We have seen the notion of set. We have seen examples of finite sets
> and infinite sets.
Hi,
I sum up, a little bit, and then I go quickly, just to provide some
motivation for the sequel.
We have seen the notion of set. We have seen examples of finite sets
and infinite sets.
For example the sets
A = {0, 1, 2},
B = {2, 3}
are finite.
The set N = {0, 1, 2, 3, ...} is infinite
ng. Thanks for the lesson.
marty a.
- Original Message -
From: "Mirek Dobsicek"
To:
Sent: Saturday, August 22, 2009 11:05 AM
Subject: Re: The seven step series
>
> Marty,
>
> If I can ask, I'd be really interested what do you think of
m.a. wrote:
> 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.
[...]
Marty,
If I can ask, I'd be really interested what do you think of this
socratic experiment
http://www.garl
>
> marty
> a.
>
>
>
>
>
>
>
>
>
> - Original Message -
> From: "Bruno Marchal"
> To:
> Sent: Friday, Aug
ource of constant fascination. Best,
marty a.
- Original Message -
From: "Bruno Marchal"
To:
Sent: Friday, August 21, 2009 3:47 AM
Subject: Re: The seven step series
>
>
> On 21 Aug 2009, at 01:24, meekerdb @
On 21 Aug 2009, at 01:24, meekerdb @dslextreme.com wrote:
>
> On Thu, Aug 20, 2009 at 12:32 PM, Bruno Marchal
> 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.
>
On Thu, Aug 20, 2009 at 12:32 PM, Bruno Marchal 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
Hi,
I give the solution of the first of the last exercises.
I reason aloud. I go slowly for those who did not get some math
courses, or just forget them. I cannot stress the importance of the
notion of bijection in the "mathematical discovery of the universal
machine" (the quote means t
On 19 Aug 2009, at 23:03, meekerdb @dslextreme.com wrote:
>
> On Wed, Aug 19, 2009 at 12:12 PM, Bruno Marchal
> wrote:
>>
>> Hi,
>>
>> Just a reminder, for me, and perhaps some training for you. In
>> preparation to the mathematical discovery of the universal machine.
>>
>> exercises:
> ...
>>
On Wed, Aug 19, 2009 at 12:12 PM, Bruno Marchal wrote:
>
> Hi,
>
> Just a reminder, for me, and perhaps some training for you. In
> preparation to the mathematical discovery of the universal machine.
>
> exercises:
...
>
>
> 4) Be sure that you have been convinced by Brent that there is a
>
Hi,
Just a reminder, for me, and perhaps some training for you. In
preparation to the mathematical discovery of the universal machine.
exercises:
1) count the number of bijections from a set A to itself. (= card{x
such that x is bijection from A to A})
2) describe some canonical bijection
On 13 Aug 2009, at 22:52, Brian Tenneson wrote:
>
> There is an explicit formula that maps N onto Q.. I found it some
> years
> back.
I let you find it again :)
I will perhaps give one, from N to NxN, (and then Q), but it is not
needed. Brent's bijection is perfectly defined.
Could everyo
Brent,
I said: this is food for Friday and the week-end, and you provide
already the solutions!
It is OK, and you are correct. Thanks for playing.
I add short comments. I have not much time till monday, and I intend
to come back on some issues. I will comment the important recent post
by D
There is an explicit formula that maps N onto Q.. I found it some years
back.
Brent Meeker wrote:
> Bruno Marchal wrote:
>> ...
>>> 4) Key questions for the sequel, on which you can meditate:
>>>
>>> - is there a bijection between N and NxN? (NxN = the cartesian
>>> product of N with N)
Bruno Marchal wrote:
...
4) Key questions for the sequel, on which you can meditate:
- is there a bijection between N and NxN? (NxN = the cartesian
product of N with N)
- is there a bijection between N and N^N?
You're making me think, Bruno. :-)
A bijection betwe
On 12 Aug 2009, at 19:55, Bruno Marchal wrote:
>
> 1) Convince yourself that if A and B are finite sets, then there
> exists a bijection between A and B if and only if card(A) = card(B).
Only you can convince yourself. I try to help by going very slowly,
but people should really mind it y
On 11 Aug 2009, at 22:24, Mirek Dobsicek wrote:
>
>
>> Well, A^B is the set of functions from B to A. By definition of set
>> exponentiation.
>
> I'd just like to point out that Bruno in his previous post in the
> seven
> step serii made a small typo
>
> "A^B - the set of all functions from A t
On 11 Aug 2009, at 22:24, Mirek Dobsicek wrote:
>
>
>> Well, A^B is the set of functions from B to A. By definition of set
>> exponentiation.
>
> I'd just like to point out that Bruno in his previous post in the
> seven
> step serii made a small typo
>
> "A^B - the set of all functions from A
> Well, A^B is the set of functions from B to A. By definition of set
> exponentiation.
I'd just like to point out that Bruno in his previous post in the seven
step serii made a small typo
"A^B - the set of all functions from A to B."
It should have been from B to A. The latest post is corr
On 11 Aug 2009, at 15:32, Mirek Dobsicek wrote:
>
>
>> 3) compute { } ^ { } and card({ } ^ { })
>
>> If card(A) = n, and card(B) = m. What is
>> card(A^B)?
>
> I find it neat to write | {} ^ {} | = | { {} } | = 1 :-)
You will make panic those who are not familiar with symbols!
>
> It's almost
> 3) compute { } ^ { } and card({ } ^ { })
> If card(A) = n, and card(B) = m. What is
> card(A^B)?
I find it neat to write | {} ^ {} | = | { {} } | = 1 :-)
It's almost like ASCII art. Just wanted to signal that I'm following.
mirek
--~--~-~--~~~---~--~~
You re
Well, given that nobody dare to ask question, I will play the role of
the idiot myself.
On 30 Jul 2009, at 21:22, Bruno Marchal wrote:
>
>
>
> Exercise:
>
>
> 1) how many functions and what are they, from the set {0, 1} to
> himself. What are the functions from {0, 1) to {0, 1}?
>
> Solut
Bruno, just to take off some mal-deserved feathers:
I think Theaetetus has two different 'e' sounds one after the other (anybody
can pronounce him better?) and in Hungarian we have them (' e ' like in
'have' and e' like in 'take') with a 3rd variation where the accent is not
applied: a closed and a
Hi Mirek,
On 05 Aug 2009, at 00:52, Mirek Dobsicek wrote:
> I've ordered the dialogue from a second-hand book shop :-) The
> Stanford
> encyclopedia says
> "Arguably, it is his (Plato) greatest work on anything."
> So I'll give it a try :-)
I love that book, and it is also my favorite piece
Hi Bruno,
Bruno Marchal wrote:
> Hi Mirek,
>
> Long and perhaps key post.
Thank you a lot for a prompt and long reply. I am digesting it :-)
Just some quick comments.
> There is no shame in being ignorant. Only in staying ignorant :)
I've ordered the dialogue from a second-hand book shop :-)
Hi Mirek,
Long and perhaps key post.
On 04 Aug 2009, at 15:32, Mirek Dobsicek wrote:
>
>
>> Come on Mirek: "Theaetetical" is an adjective I have forged from
>> "Theatetus".
>> "Theatetus" gives 195.000 results on Google.
>> "Theatetus" wiki 4310.
>
> Of course, after all you reference the dialog
John,
Thanks for those informations. I thought that the "æ" was just a
french, if not an old french, usage.
Note that when I wrote "Theatetus", it is just a mispelling. I tend to
forget that second "e", but your remark will help me to remind it.
Note that Miles Burnyeat, in his book " The Th
> Come on Mirek: "Theaetetical" is an adjective I have forged from
> "Theatetus".
> "Theatetus" gives 195.000 results on Google.
> "Theatetus" wiki 4310.
Of course, after all you reference the dialogue Theaetetus in your
papers thus one can easily match the word Theaetetical agains it.
Let me qu
Bruno and Mirek,
concerning Theateticus vs. Theaeteticus:
in my strange linguistic background I make a difference betwee ai and ae -
the spelling in Greek and Latin of the name. As far as I know, nobody knows
for sure how did the 'ancient' Greeks pronounce their ai - maybe as the flat
'e' like in
On 02 Aug 2009, at 23:20, Mirek Dobsicek wrote:
>
>
>>> I am in a good mood and a bit picky :-) Do you know how many entries
>>> google gave me upon entering
>>> Theaetetical -marchal -bruno
>>
>>
>> Well 144?
>>
>> Good way to find my papers on that. The pages refer quickly to this
>> list or th
>> I am in a good mood and a bit picky :-) Do you know how many entries
>> google gave me upon entering
>> Theaetetical -marchal -bruno
>
>
> Well 144?
>
> Good way to find my papers on that. The pages refer quickly to this
> list or the FOR list.
I am sorry for the delay, I've just got bac
Hi John, and the other.
John motivates me to explain what is a function, "for a mathematician".
On 30 Jul 2009, at 17:53, John Mikes wrote:
> Hi, Bruno,
> let me skip the technical part
OK. But I remind you this current thread *is* technical.
> and jump on the following text.
> F u n c t i
Hi, Bruno,
let me skip the technical part and jump on the following text.
*F u n c t i o n* as I believe is - for you - the y = f(x) *form*. For me:
the *activity -* shown when plotting on a coordinate system the f(x) values
of the Y-s to the values on the x-axle resulting in a relation (curve). A
SOLUTIONS
OK. I give the solution of the exercises of the last session, on the
cartesian product of sets.
I recall the definition of the product A X B.
A X B= {(x,y) such that x belongs to A and y belongs to B}
I gave A = {0, 1}, and B = {a, b}.
In this case, A X B = {(0,a), (0, b)
Ronald,
On 28 Jul 2009, at 12:51, ronaldheld wrote:
>
> Bruno:
> I meant the mathematical formalism you are teaching us. When we
> eventually get to the UDA steps, I wil be better able to do that
> assessment.
>
OK.
Note that the first 6 steps have already be done recently, with Kim,
and even
On 28 Jul 2009, at 17:36, m.a. wrote:
> Bruno,
> I have searched my notes for an exposition of BIJECTION
> and found only one mention in an early email which promises to
> define it in a later lesson. Do you have a reference to that lesson
> or perhaps an instant explanation of
,
Chief Ignoramus
- Original Message -
From: "Bruno Marchal"
To:
Sent: Monday, July 27, 2009 4:54 PM
Subject: Re: The seven step series
>
> We have discovered SBIJECTION between powersets of a set with cardinal
l me if my last post, on the relation
>
> >> (a^n) * (a^m) = a^(n + m)
>
> >> did help you.
>
> >> You are lucky to have an infinitely patient teacher. You can ask any
> >> question, like "Bruno,
>
> >> is (a^n) * (a^m) the same a
Hi,
OK, I will come back on the square root of 2 later.
We have talked on sets.
Sets have elements, and elements of a set define completely the set,
and a set is completely defined by its elements.
Example: here is a set of numbers {1, 2, 3}
and a set of sets of numbers {{1, 2}, {3}, { }}.
t;>
>> You are lucky to have an infinitely patient teacher. You can ask any
>> question, like "Bruno,
>>
>> is (a^n) * (a^m) the same as a^n times a^m?"
>> Answer: yes, I use often "*", "x", as shorthand for "times", and I
>
s a^n times a^m?"
> Answer: yes, I use often "*", "x", as shorthand for "times", and I
> use "(" and ")" as delimiters in case I fear some ambiguity.
>
> Bruno
>
>
>
>
>
>
>
> > -- Original Message ---
quot;)" as delimiters in case I fear some ambiguity.
Bruno
>
>
>
>
> -- Original Message -----
> From: Bruno Marchal
> To: everything-list@googlegroups.com
> Sent: Wednesday, July 22, 2009 12:20 PM
> Subject: Re: The seven step series
>
> Marty,
>
> Br
at 14:02, m.a. wrote:
> Hi Bruno,
> I asked Brent Meeker a question which he referred
> back to you. Will you be covering it? (see para in bold below)
>
> - Original Message -
> From: "Brent Meeker"
> To:
> Sent: Wednesday, July 22, 2009 11:4
o Marchal
To: everything-list@googlegroups.com
Sent: Wednesday, July 22, 2009 12:20 PM
Subject: Re: The seven step series
Marty,
Brent wrote:
On 21 Jul 2009, at 23:24, Brent Meeker wrote:
Take all strings of length 2
00 01 10 11
Hi Bruno,
I asked Brent Meeker a question which he referred back to you.
Will you be covering it? (see para in bold below)
- Original Message -
From: "Brent Meeker"
To:
Sent: Wednesday, July 22, 2009 11:49 PM
Subject: Re: The seven step series
>> *000
m.a. wrote:
> *Going a step further... (see below)*
> **
> - Original Message -
> From: "Brent Meeker" <mailto:meeke...@dslextreme.com>>
> To: <mailto:everything-list@googlegroups.com>>
> Sent: Wednesday, July 22, 2009 12:57 PM
> Su
Going a step further... (see below)
- Original Message -
From: "Brent Meeker"
To:
Sent: Wednesday, July 22, 2009 12:57 PM
Subject: Re: The seven step series
>
> m.a. wrote:
>> Hi Brent,
>> I really appreciate the help and I hate to imp
googlegroups.com>>
> Sent: Tuesday, July 21, 2009 5:24 PM
> Subject: Re: The seven step series
>
> >
> > Take all strings of length 2
> > 00 01 10 11
> > Make two copies of each
> > 00 00 01
Marty,
Brent wrote:
On 21 Jul 2009, at 23:24, Brent Meeker wrote:
>
> Take all strings of length 2
> 00 01 10 11
> Make two copies of each
> 00 00 01 01 10 10 11 11
> Add a 0 to the first and a 1 to the second
> 000
Hi Brent,
I really appreciate the help and I hate to impose on your
patience but...(see below)
- Original Message -
From: "Brent Meeker"
To:
Sent: Tuesday, July 21, 2009 5:24 PM
Subject: Re: The seven step series
>
> Take all strings of length 2
>
-
> From: "Brent Meeker" <mailto:meeke...@dslextreme.com>>
> To: <mailto:everything-list@googlegroups.com>>
> Sent: Tuesday, July 21, 2009 3:57 PM
> Subject: Re: The seven step series
>
> >
> > Each binary string of length n has two possible
09 3:57 PM
Subject: Re: The seven step series
>
> Each binary string of length n has two possible continuations of length
> n+1, one of them by appending a 0 and one of them by appending a 1. So
> to get all binary strings of length n+1 take each string of length n,
> make two copie
>
> - Original Message -
> *From:* Bruno Marchal <mailto:marc...@ulb.ac.be>
> *To:* everything-list@googlegroups.com
> <mailto:everything-list@googlegroups.com>
> *Sent:* Monday, July 20, 2009 3:17 PM
> *Subject:* Re: The seven step seri
everything-list@googlegroups.com
Sent: Monday, July 20, 2009 3:17 PM
Subject: Re: The seven step series
On 20 Jul 2009, at 15:34, m.a. wrote:
And then we have seen that such cardinal was given by 2^n.
You can see this directly by seeing that adding an element in a set, double
the number of
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