| Topic: |
Religions > Atheism |
| User: |
"Uncle Buck" |
| Date: |
23 Sep 2005 11:04:21 PM |
| Object: |
Why infinity equals zero? |
This is a mental game I'm playing at the moment as I dig for deeper
"truths", so please bear with me.
Existence can be defined by innumerable parameters. One of the
parameters - mentioned in the "something from nothing" post - is the
degree of precision necessary for maintaining the existence of
something.
In that post, I noted (in slightly fewer words) the observation that
the more precise a set of parameters must be in order for the
existence of something to be defined, the less stable the existence of
that something becomes as defined by that parameter set.
With regard to the degree of precision necessary to maintain a "True
Nothing" and the degree of precision necessary to maintain a "Truly
Infinite", both are precisely equal. Both "True Nothing" and "Truly
Infinite" are very specific parameter sets, the integrity of which
_any_ deviation obliviates.
Perhaps we've been focussing on the wrong sort of quality when trying
to figure existence out. We look at temperature, mass, volume, etc...
But those things don't really define what is happening so much as they
seem to define the _results_ of what is happening. Is there a set of
cognitive empirical tools one might utilize to study reality more
directly, one that includes such things as "degree of precision
necessary to define the phenomenon in question"? One that seeks to
infer some of the qualitative aspects of existence based upon the
techniques used to observe it?
I know it's not very "scientific" or "detailed", but I think it could
become so. This train of thought is just beginning, after all. With
regard to infinity and zero, might something such as what can be
inferred from the above line of thinking be behind the success of the
practice of "simplification"?
--
L8r,
Uncle Buck
_o-O=~_o-O=~_o-O=~_o-O=~_o-O=~_o-O=~_o-O=
Those first to step up and say,
"Now is not the time for placing blame"
...
...are quite often to blame....
_o-O=~_o-O=~_o-O=~_o-O=~_o-O=~_o-O=~_o-O=
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| User: "Josef Balluch" |
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| Title: Re: Why infinity equals zero? |
24 Sep 2005 01:59:37 PM |
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"Uncle Buck" <UncleBuck@SpamMeNot.com> wrote in message
news:68j9j1hbpv76ecuottu1j2htqrjok9k6ge@4ax.com...
....
Existence can be defined by innumerable parameters.
On the contrary, I do not see that existence can have any parameters, since
there would seem to be only one "kind" of existence. Properties distinguish
between things, but if there is only one kind of existence then there is no
need to distinguish it from another kind.
One of the
parameters - mentioned in the "something from nothing" post - is the
degree of precision necessary for maintaining the existence of
something.
In that post, I noted (in slightly fewer words) the observation that
the more precise a set of parameters must be in order for the
existence of something to be defined, the less stable the existence of
that something becomes as defined by that parameter set.
As I pointed out in that thread, your description of the relationship
between precision and stability is mistaken.
With regard to the degree of precision necessary to maintain a "True
Nothing" and the degree of precision necessary to maintain a "Truly
Infinite", both are precisely equal.
As I pointed out, it is not clear that "nothing" would require maintenance.
Both "True Nothing" and "Truly
Infinite" are very specific parameter sets, the integrity of which
_any_ deviation obliviates.
As we know from the example of Hilbert's Hotel, you can easily add or take
away from an infinite set.
Perhaps we've been focussing on the wrong sort of quality when trying
to figure existence out. We look at temperature, mass, volume, etc...
But those things don't really define what is happening so much as they
seem to define the _results_ of what is happening.
Yes. As I mentioned earlier, existence would have no properties.
Is there a set of
cognitive empirical tools one might utilize to study reality more
directly, one that includes such things as "degree of precision
necessary to define the phenomenon in question"?
We already have many tools for studying reality. Did you perhaps intend to
say "study existence"? It is doubtful if we could study existence in this
way. Having no properties, existence cannot be examined empirically.
One that seeks to
infer some of the qualitative aspects of existence based upon the
techniques used to observe it?
Existence has no "qualitative aspects".
....
Regards,
Josef
.
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| User: "Gregory Gadow" |
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| Title: Re: Why infinity equals zero? |
26 Sep 2005 08:39:36 AM |
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By an engineer's definition, infinity is at least one more than you care
to deal with at the moment. Since zero is nothing, infinity can not be
zero (unless you are working exclusively with -1, at which point both zero
and infinity are irrelevant.)
--
Gregory Gadow
techbear@serv.net
http://www.serv.net/~techbear
"Without faith we might relapse into scientific or rational thinking,
which leads by a slippery slope toward constitutional democracy."
- Robert Anton Wilson
.
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| User: "Liz" |
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| Title: Re: Why infinity equals zero? |
24 Sep 2005 06:52:34 AM |
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On Fri, 23 Sep 2005 21:04:21 -0700, Uncle Buck
<UncleBuck@SpamMeNot.com> in news message
<68j9j1hbpv76ecuottu1j2htqrjok9k6ge@4ax.com> wrote:
This is a mental game I'm playing at the moment as I dig for deeper
"truths", so please bear with me.
Existence can be defined by innumerable parameters. One of the
parameters - mentioned in the "something from nothing" post - is the
degree of precision necessary for maintaining the existence of
something.
In that post, I noted (in slightly fewer words) the observation that
the more precise a set of parameters must be in order for the
existence of something to be defined, the less stable the existence of
that something becomes as defined by that parameter set.
With regard to the degree of precision necessary to maintain a "True
Nothing" and the degree of precision necessary to maintain a "Truly
Infinite", both are precisely equal. Both "True Nothing" and "Truly
Infinite" are very specific parameter sets, the integrity of which
_any_ deviation obliviates.
You are overlooking the fact that all infinite sets are not equal.
For example: You have an infinite set of books. Included in that
infinite set of books are an infinite set of black books, an infinite
set of blue books, and an infinite set of yellow books.
If all of these are infinite, is the infinite set of yellow books
smaller or larger than the infinite set of all books?
Überwench #658 Now a *real* atheist!
Dame Liz the Undaunted Ath.D BAAWA
Charter Member of SMASH
and Queen of the known universe
.
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| User: "Kevin Anthoney" |
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| Title: Re: Why infinity equals zero? |
24 Sep 2005 07:25:54 AM |
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Liz wrote:
On Fri, 23 Sep 2005 21:04:21 -0700, Uncle Buck
<UncleBuck@SpamMeNot.com> in news message
<68j9j1hbpv76ecuottu1j2htqrjok9k6ge@4ax.com> wrote:
This is a mental game I'm playing at the moment as I dig for deeper
"truths", so please bear with me.
Existence can be defined by innumerable parameters. One of the
parameters - mentioned in the "something from nothing" post - is the
degree of precision necessary for maintaining the existence of
something.
In that post, I noted (in slightly fewer words) the observation that
the more precise a set of parameters must be in order for the
existence of something to be defined, the less stable the existence of
that something becomes as defined by that parameter set.
With regard to the degree of precision necessary to maintain a "True
Nothing" and the degree of precision necessary to maintain a "Truly
Infinite", both are precisely equal. Both "True Nothing" and "Truly
Infinite" are very specific parameter sets, the integrity of which
_any_ deviation obliviates.
You are overlooking the fact that all infinite sets are not equal.
True, but the example below is a bad one.
For example: You have an infinite set of books. Included in that
infinite set of books are an infinite set of black books, an infinite
set of blue books, and an infinite set of yellow books.
If all of these are infinite, is the infinite set of yellow books
smaller or larger than the infinite set of all books?
You can apply labels { 1, 2, 3, ... } to each of the yellow books - there's
a one-to-one mapping between the set of positive integers and the set of
yellow books. Likewise, there's a one-to-one mapping between the set of
positive integers and the set of all books. So we have:
{ yellow books } <-> { 1, 2, 3, ... } <-> { all books }
where "<->" implies a one-to-one mapping. Hence we have
{ yellow books } <-> { all books },
so there are actually the same number of yellow books as there are books
altogether, despite the fact there are an infinite number of black and blue
books thrown in there as well.
So There.
--
Kevin Anthoney
kanthoney[a]dsl.pipex.com
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| User: "Pramod Subramanyan" |
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| Title: Re: Why infinity equals zero? |
25 Sep 2005 12:09:36 AM |
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Kevin Anthoney wrote:
snip quote <<
You can apply labels { 1, 2, 3, ... } to each of the yellow books - there's
a one-to-one mapping between the set of positive integers and the set of
yellow books. Likewise, there's a one-to-one mapping between the set of
positive integers and the set of all books. So we have:
{ yellow books } <-> { 1, 2, 3, ... } <-> { all books }
where "<->" implies a one-to-one mapping. Hence we have
{ yellow books } <-> { all books },
so there are actually the same number of yellow books as there are books
altogether, despite the fact there are an infinite number of black and blue
books thrown in there as well.
I don't agree with this. Basically you're assuming that the size of one
infinite set equals the size of another infinite set, which is
definitely not true. From the mathematical point of view, you CAN NOT
compare infinity with infinity. Pure mathematicians will tell you that
infinity is a bad thing and everybody agrees that it has to be handled
carefully.
So There.
--
Kevin Anthoney
kanthoney[a]dsl.pipex.com
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| User: "Kevin Anthoney" |
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| Title: Re: Why infinity equals zero? |
25 Sep 2005 10:26:24 AM |
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Pramod Subramanyan wrote:
Kevin Anthoney wrote:
snip quote <<
You can apply labels { 1, 2, 3, ... } to each of the yellow books -
there's a one-to-one mapping between the set of positive integers and the
set of
yellow books. Likewise, there's a one-to-one mapping between the set of
positive integers and the set of all books. So we have:
{ yellow books } <-> { 1, 2, 3, ... } <-> { all books }
where "<->" implies a one-to-one mapping. Hence we have
{ yellow books } <-> { all books },
so there are actually the same number of yellow books as there are books
altogether, despite the fact there are an infinite number of black and
blue books thrown in there as well.
I don't agree with this.
Fair enough, but what I described was the standard way that mathematicians
deal with infinite sets.
Basically you're assuming that the size of one
infinite set equals the size of another infinite set, which is
definitely not true.
I assumed no such thing - in fact, in general that's not true. For example,
the set of real numbers is larger than the number of integers, one proof
being Cantor's "diagonal slash" argument.
From the mathematical point of view, you CAN NOT
compare infinity with infinity.
Sure you can. Read up on Set Theory, in particular the cardinality of sets.
Pure mathematicians will tell you that
infinity is a bad thing and everybody agrees that it has to be handled
carefully.
So There.
--
Kevin Anthoney
kanthoney[a]dsl.pipex.com
--
Kevin Anthoney
kanthoney[a]dsl.pipex.com
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| User: "Gregory Gadow" |
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| Title: Re: Why infinity equals zero? |
26 Sep 2005 08:57:11 AM |
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Kevin Anthoney wrote:
Pramod Subramanyan wrote:
Kevin Anthoney wrote:
snip quote <<
You can apply labels { 1, 2, 3, ... } to each of the yellow books -
there's a one-to-one mapping between the set of positive integers and the
set of
yellow books. Likewise, there's a one-to-one mapping between the set of
positive integers and the set of all books. So we have:
{ yellow books } <-> { 1, 2, 3, ... } <-> { all books }
where "<->" implies a one-to-one mapping. Hence we have
{ yellow books } <-> { all books },
so there are actually the same number of yellow books as there are books
altogether, despite the fact there are an infinite number of black and
blue books thrown in there as well.
I don't agree with this.
Fair enough, but what I described was the standard way that mathematicians
deal with infinite sets.
Basically you're assuming that the size of one
infinite set equals the size of another infinite set, which is
definitely not true.
I assumed no such thing - in fact, in general that's not true. For example,
the set of real numbers is larger than the number of integers, one proof
being Cantor's "diagonal slash" argument.
I don't think I've ever seen that one. I do remember this little bit of logical
masturbation, though:
Take the set of all positive integers. Call it A.
Take the set of all positive even integers. Call it B.
Every element B(x) is a member of A. There are elements A(x) which are not
members of B. Therefore, A is larger, and it can be shown that the sum
[A(0...infinity)] -> (2 * sum[B(0...infinity)])
HOWEVER
For every element A(x) there is a corresponding element B(x) such that A(x) * 2
= B(x). Therefore, B is larger such that sum[B(0...infinity)] = (2 *
sum[A(0...infinity)])
The fact that BOTH assertions can be logically proven is why mathematicians hate
infinities.
From the mathematical point of view, you CAN NOT
compare infinity with infinity.
Sure you can. Read up on Set Theory, in particular the cardinality of sets.
Aaaahhhh! I remember that one from abstract algebra in college. I remember the
mystical crap one of my classmates spouted about how the logical excercise of
creating the field of complex numbers out of the empty set "proves" that God
created the universe ex nihilo.
--
Gregory Gadow
techbear@serv.net
http://www.serv.net/~techbear
"Without faith we might relapse into scientific or rational thinking,
which leads by a slippery slope toward constitutional democracy."
- Robert Anton Wilson
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| User: "Liz" |
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| Title: Re: Why infinity equals zero? |
25 Sep 2005 11:01:19 AM |
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On Sat, 24 Sep 2005 13:25:54 +0100, Kevin Anthoney
<kevin_anthoney@hotmail.com> in news message
<BbWdncwDDZRJ2KjeRVnyrQ@pipex.net> wrote:
You can apply labels { 1, 2, 3, ... } to each of the yellow books - there's
a one-to-one mapping between the set of positive integers and the set of
yellow books. Likewise, there's a one-to-one mapping between the set of
positive integers and the set of all books. So we have:
{ yellow books } <-> { 1, 2, 3, ... } <-> { all books }
where "<->" implies a one-to-one mapping. Hence we have
{ yellow books } <-> { all books },
so there are actually the same number of yellow books as there are books
altogether, despite the fact there are an infinite number of black and blue
books thrown in there as well.
So There.
However when you map the set of yellow books to the set of books,
there is a one to one mapping between the yellow books in the yellow
book set to the yellow books in the book set. IOW, since the set of
yellow books is a subset of the set of books, then each yellow book in
the yellow book set corresponds with itself in the set of all books,
thusly:
Yellow Books All Books
Y1 Y1
Y2 Y2
Y3 Y3
. .
. .
. .
Given that each yellow book in the subset corresponds to itself in the
larger set, which yellow book maps on a one to one correspondence to a
the first black book instead of itself?
Y? B1
Überwench #658 Now a *real* atheist!
Dame Liz the Undaunted Ath.D BAAWA
Charter Member of SMASH
and Queen of the known universe
.
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| User: "Fred Stone" |
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| Title: Re: Why infinity equals zero? |
25 Sep 2005 11:24:26 AM |
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Liz <ehuth1@donotspam.com> wrote in
news:nrhdj1pmi4nekp3roiug45o0p0ccm5djpd@4ax.com:
On Sat, 24 Sep 2005 13:25:54 +0100, Kevin Anthoney
<kevin_anthoney@hotmail.com> in news message
<BbWdncwDDZRJ2KjeRVnyrQ@pipex.net> wrote:
You can apply labels { 1, 2, 3, ... } to each of the yellow books -
there's a one-to-one mapping between the set of positive integers and
the set of yellow books. Likewise, there's a one-to-one mapping
between the set of positive integers and the set of all books. So we
have:
{ yellow books } <-> { 1, 2, 3, ... } <-> { all books }
where "<->" implies a one-to-one mapping. Hence we have
{ yellow books } <-> { all books },
so there are actually the same number of yellow books as there are
books altogether, despite the fact there are an infinite number of
black and blue books thrown in there as well.
So There.
However when you map the set of yellow books to the set of books,
there is a one to one mapping between the yellow books in the yellow
book set to the yellow books in the book set. IOW, since the set of
yellow books is a subset of the set of books, then each yellow book in
the yellow book set corresponds with itself in the set of all books,
thusly:
Yellow Books All Books
Y1 Y1
Y2 Y2
Y3 Y3
. .
. .
. .
Given that each yellow book in the subset corresponds to itself in the
larger set, which yellow book maps on a one to one correspondence to a
the first black book instead of itself?
Y? B1
Let's label the three colors y=Yellow, b=Black, and u=blUe.
Then just change the mapping to be y1->y1; y2->b1; y3->u1;...
--
Fred Stone
aa# 1369
"This city, for the first time that I can remember,
is drug-free and violence-free.
And we plan to keep it that way." - Mayor Ray Nagin
.
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| User: "Liz" |
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| Title: Re: Why infinity equals zero? |
25 Sep 2005 11:46:48 AM |
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On Sun, 25 Sep 2005 16:24:26 GMT, Fred Stone <fstone69@earthling.com>
in news message <1127665466.ce64d0252510b39835b87b48cf4eb381@teranews>
wrote:
Liz <ehuth1@donotspam.com> wrote in
news:nrhdj1pmi4nekp3roiug45o0p0ccm5djpd@4ax.com:
On Sat, 24 Sep 2005 13:25:54 +0100, Kevin Anthoney
<kevin_anthoney@hotmail.com> in news message
<BbWdncwDDZRJ2KjeRVnyrQ@pipex.net> wrote:
You can apply labels { 1, 2, 3, ... } to each of the yellow books -
there's a one-to-one mapping between the set of positive integers and
the set of yellow books. Likewise, there's a one-to-one mapping
between the set of positive integers and the set of all books. So we
have:
{ yellow books } <-> { 1, 2, 3, ... } <-> { all books }
where "<->" implies a one-to-one mapping. Hence we have
{ yellow books } <-> { all books },
so there are actually the same number of yellow books as there are
books altogether, despite the fact there are an infinite number of
black and blue books thrown in there as well.
So There.
However when you map the set of yellow books to the set of books,
there is a one to one mapping between the yellow books in the yellow
book set to the yellow books in the book set. IOW, since the set of
yellow books is a subset of the set of books, then each yellow book in
the yellow book set corresponds with itself in the set of all books,
thusly:
Yellow Books All Books
Y1 Y1
Y2 Y2
Y3 Y3
. .
. .
. .
Given that each yellow book in the subset corresponds to itself in the
larger set, which yellow book maps on a one to one correspondence to a
the first black book instead of itself?
Y? B1
Let's label the three colors y=Yellow, b=Black, and u=blUe.
Then just change the mapping to be y1->y1; y2->b1; y3->u1;...
And then ? ->y2 ; ? -> y3
Überwench #658 Now a *real* atheist!
Dame Liz the Undaunted Ath.D BAAWA
Charter Member of SMASH
and Queen of the known universe
.
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| User: "Fred Stone" |
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| Title: Re: Why infinity equals zero? |
25 Sep 2005 02:44:06 PM |
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Liz <ehuth1@donotspam.com> wrote in
news:oqkdj1pgcl7dgg0ml5sevnngosvoj17nvp@4ax.com:
On Sun, 25 Sep 2005 16:24:26 GMT, Fred Stone <fstone69@earthling.com>
in news message <1127665466.ce64d0252510b39835b87b48cf4eb381@teranews>
wrote:
Liz <ehuth1@donotspam.com> wrote in
news:nrhdj1pmi4nekp3roiug45o0p0ccm5djpd@4ax.com:
On Sat, 24 Sep 2005 13:25:54 +0100, Kevin Anthoney
<kevin_anthoney@hotmail.com> in news message
<BbWdncwDDZRJ2KjeRVnyrQ@pipex.net> wrote:
You can apply labels { 1, 2, 3, ... } to each of the yellow books -
there's a one-to-one mapping between the set of positive integers
and
the set of yellow books. Likewise, there's a one-to-one mapping
between the set of positive integers and the set of all books. So
we
have:
{ yellow books } <-> { 1, 2, 3, ... } <-> { all books }
where "<->" implies a one-to-one mapping. Hence we have
{ yellow books } <-> { all books },
so there are actually the same number of yellow books as there are
books altogether, despite the fact there are an infinite number of
black and blue books thrown in there as well.
So There.
However when you map the set of yellow books to the set of books,
there is a one to one mapping between the yellow books in the yellow
book set to the yellow books in the book set. IOW, since the set of
yellow books is a subset of the set of books, then each yellow book
in
the yellow book set corresponds with itself in the set of all books,
thusly:
Yellow Books All Books
Y1 Y1
Y2 Y2
Y3 Y3
. .
. .
. .
Given that each yellow book in the subset corresponds to itself in
the
larger set, which yellow book maps on a one to one correspondence to
a
the first black book instead of itself?
Y? B1
Let's label the three colors y=Yellow, b=Black, and u=blUe.
Then just change the mapping to be y1->y1; y2->b1; y3->u1;...
And then ? ->y2 ; ? -> y3
y(3x-2)->yx; y(3x-1)->bx; y(3x)->ux;
So y4->y2 and y7->y3
--
Fred Stone
aa# 1369
"This city, for the first time that I can remember,
is drug-free and violence-free.
And we plan to keep it that way." - Mayor Ray Nagin
.
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| User: "Gregory Gadow" |
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| Title: Re: Why infinity equals zero? |
26 Sep 2005 08:59:26 AM |
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Fred Stone wrote:
Liz <ehuth1@donotspam.com> wrote in
news:oqkdj1pgcl7dgg0ml5sevnngosvoj17nvp@4ax.com:
On Sun, 25 Sep 2005 16:24:26 GMT, Fred Stone <fstone69@earthling.com>
in news message <1127665466.ce64d0252510b39835b87b48cf4eb381@teranews>
wrote:
Liz <ehuth1@donotspam.com> wrote in
news:nrhdj1pmi4nekp3roiug45o0p0ccm5djpd@4ax.com:
On Sat, 24 Sep 2005 13:25:54 +0100, Kevin Anthoney
<kevin_anthoney@hotmail.com> in news message
<BbWdncwDDZRJ2KjeRVnyrQ@pipex.net> wrote:
You can apply labels { 1, 2, 3, ... } to each of the yellow books -
there's a one-to-one mapping between the set of positive integers
and
the set of yellow books. Likewise, there's a one-to-one mapping
between the set of positive integers and the set of all books. So
we
have:
{ yellow books } <-> { 1, 2, 3, ... } <-> { all books }
where "<->" implies a one-to-one mapping. Hence we have
{ yellow books } <-> { all books },
so there are actually the same number of yellow books as there are
books altogether, despite the fact there are an infinite number of
black and blue books thrown in there as well.
So There.
However when you map the set of yellow books to the set of books,
there is a one to one mapping between the yellow books in the yellow
book set to the yellow books in the book set. IOW, since the set of
yellow books is a subset of the set of books, then each yellow book
in
the yellow book set corresponds with itself in the set of all books,
thusly:
Yellow Books All Books
Y1 Y1
Y2 Y2
Y3 Y3
. .
. .
. .
Given that each yellow book in the subset corresponds to itself in
the
larger set, which yellow book maps on a one to one correspondence to
a
the first black book instead of itself?
Y? B1
Let's label the three colors y=Yellow, b=Black, and u=blUe.
Then just change the mapping to be y1->y1; y2->b1; y3->u1;...
And then ? ->y2 ; ? -> y3
y(3x-2)->yx; y(3x-1)->bx; y(3x)->ux;
So y4->y2 and y7->y3
Except that x is not a member of the set of all books, which you yourself
have defined as the union the sets y, b and u. Dare I say it... you are
outside of your field on this ;-p
--
Gregory Gadow
techbear@serv.net
http://www.serv.net/~techbear
"Without faith we might relapse into scientific or rational thinking,
which leads by a slippery slope toward constitutional democracy."
- Robert Anton Wilson
.
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| User: "Kevin Anthoney" |
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| Title: Re: Why infinity equals zero? |
25 Sep 2005 12:55:59 PM |
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Liz wrote:
On Sat, 24 Sep 2005 13:25:54 +0100, Kevin Anthoney
<kevin_anthoney@hotmail.com> in news message
<BbWdncwDDZRJ2KjeRVnyrQ@pipex.net> wrote:
You can apply labels { 1, 2, 3, ... } to each of the yellow books -
there's a one-to-one mapping between the set of positive integers and the
set of
yellow books. Likewise, there's a one-to-one mapping between the set of
positive integers and the set of all books. So we have:
{ yellow books } <-> { 1, 2, 3, ... } <-> { all books }
where "<->" implies a one-to-one mapping. Hence we have
{ yellow books } <-> { all books },
so there are actually the same number of yellow books as there are books
altogether, despite the fact there are an infinite number of black and
blue books thrown in there as well.
So There.
However when you map the set of yellow books to the set of books,
there is a one to one mapping between the yellow books in the yellow
book set to the yellow books in the book set. IOW, since the set of
yellow books is a subset of the set of books, then each yellow book in
the yellow book set corresponds with itself in the set of all books,
thusly:
Yellow Books All Books
Y1 Y1
Y2 Y2
Y3 Y3
. .
. .
. .
Given that each yellow book in the subset corresponds to itself in the
larger set, which yellow book maps on a one to one correspondence to a
the first black book instead of itself?
With that particular mapping, none of them. The important thing about
measuring infinite sets, though, is whether *any* mapping exists that is
one to one - if there is such a mapping, then the sets are the same size
(or "cardinality"). The fact that there are loads of other mappings that
aren't one-to-one is deemed not to matter.
Y? B1
--
Kevin Anthoney
kanthoney[a]dsl.pipex.com
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| User: "Uncle Buck" |
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| Title: Re: Why infinity equals zero? |
24 Sep 2005 10:12:34 AM |
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On Sat, 24 Sep 2005 11:52:34 GMT, Liz <ehuth1@donotspam.com> wrote:
On Fri, 23 Sep 2005 21:04:21 -0700, Uncle Buck
<UncleBuck@SpamMeNot.com> in news message
<68j9j1hbpv76ecuottu1j2htqrjok9k6ge@4ax.com> wrote:
This is a mental game I'm playing at the moment as I dig for deeper
"truths", so please bear with me.
Existence can be defined by innumerable parameters. One of the
parameters - mentioned in the "something from nothing" post - is the
degree of precision necessary for maintaining the existence of
something.
In that post, I noted (in slightly fewer words) the observation that
the more precise a set of parameters must be in order for the
existence of something to be defined, the less stable the existence of
that something becomes as defined by that parameter set.
With regard to the degree of precision necessary to maintain a "True
Nothing" and the degree of precision necessary to maintain a "Truly
Infinite", both are precisely equal. Both "True Nothing" and "Truly
Infinite" are very specific parameter sets, the integrity of which
_any_ deviation obliviates.
You are overlooking the fact that all infinite sets are not equal.
For example: You have an infinite set of books. Included in that
infinite set of books are an infinite set of black books, an infinite
set of blue books, and an infinite set of yellow books.
If all of these are infinite, is the infinite set of yellow books
smaller or larger than the infinite set of all books?
I dunno - sounds like they're "precisely equal" to me. ;-) Would
this not be yet another scenario in which simplification would work?
:-?
--
L8r,
Uncle Buck
_o-O=~_o-O=~_o-O=~_o-O=~_o-O=~_o-O=~_o-O=
Those first to step up and say,
"Now is not the time for placing blame"
...
...are quite often to blame....
_o-O=~_o-O=~_o-O=~_o-O=~_o-O=~_o-O=~_o-O=
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| User: "Ben Kaufman" |
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| Title: Re: Why infinity equals zero? |
25 Sep 2005 08:16:08 PM |
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On Sat, 24 Sep 2005 08:12:34 -0700, Uncle Buck <UncleBuck@SpamMeNot.com> wrote:
On Sat, 24 Sep 2005 11:52:34 GMT, Liz <ehuth1@donotspam.com> wrote:
On Fri, 23 Sep 2005 21:04:21 -0700, Uncle Buck
<UncleBuck@SpamMeNot.com> in news message
<68j9j1hbpv76ecuottu1j2htqrjok9k6ge@4ax.com> wrote:
This is a mental game I'm playing at the moment as I dig for deeper
"truths", so please bear with me.
Existence can be defined by innumerable parameters. One of the
parameters - mentioned in the "something from nothing" post - is the
degree of precision necessary for maintaining the existence of
something.
In that post, I noted (in slightly fewer words) the observation that
the more precise a set of parameters must be in order for the
existence of something to be defined, the less stable the existence of
that something becomes as defined by that parameter set.
With regard to the degree of precision necessary to maintain a "True
Nothing" and the degree of precision necessary to maintain a "Truly
Infinite", both are precisely equal. Both "True Nothing" and "Truly
Infinite" are very specific parameter sets, the integrity of which
_any_ deviation obliviates.
You are overlooking the fact that all infinite sets are not equal.
For example: You have an infinite set of books. Included in that
infinite set of books are an infinite set of black books, an infinite
set of blue books, and an infinite set of yellow books.
If all of these are infinite, is the infinite set of yellow books
smaller or larger than the infinite set of all books?
I dunno - sounds like they're "precisely equal" to me. ;-) Would
this not be yet another scenario in which simplification would work?
:-?
The set of all books (assuming infinite) and the set of all yellow books
(assumed to be infinite) are not equal because the set of yellow books is a
proper subset of the set of all books. The SIZE of both sets is infinite but
infinity is not a concrete value like zero.
Ben
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| User: "Pramod Subramanyan" |
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| Title: Re: Why infinity equals zero? |
24 Sep 2005 07:20:02 AM |
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Uncle Buck wrote:
This is a mental game I'm playing at the moment as I dig for deeper
"truths", so please bear with me.
Existence can be defined by innumerable parameters. One of the
parameters - mentioned in the "something from nothing" post - is the
degree of precision necessary for maintaining the existence of
something.
In that post, I noted (in slightly fewer words) the observation that
the more precise a set of parameters must be in order for the
existence of something to be defined, the less stable the existence of
that something becomes as defined by that parameter set.
With regard to the degree of precision necessary to maintain a "True
Nothing" and the degree of precision necessary to maintain a "Truly
Infinite", both are precisely equal. Both "True Nothing" and "Truly
Infinite" are very specific parameter sets, the integrity of which
_any_ deviation obliviates.
Perhaps we've been focussing on the wrong sort of quality when trying
to figure existence out.
We look at temperature, mass, volume, etc...
But those things don't really define what is happening so much as they
seem to define the _results_ of what is happening. Is there a set of
cognitive empirical tools one might utilize to study reality more
directly, one that includes such things as "degree of precision
necessary to define the phenomenon in question"?
Why should we try to "figure existence out"? The point is, the
existence thing is fairly straightforward, some things exist - some
things don't. Sometimes we can conclude that somethings exist using an
indirect approach and when are unsure of those deductions, we say has
that the probabilty that the thing exists is (say) 75.44%. The thing
can either only exist or not exist, its just our perception of the
correctness of our decision that is vaguely defined.
One that seeks to
infer some of the qualitative aspects of existence based upon the
techniques used to observe it?
This brings us back to the old questions of "why are things the way
they are?" and I've always thought the answer to that is in the
anthropic principle.
I know it's not very "scientific" or "detailed", but I think it could
become so. This train of thought is just beginning, after all. With
regard to infinity and zero, might something such as what can be
inferred from the above line of thinking be behind the success of the
practice of "simplification"?
--
L8r,
Uncle Buck
_o-O=~_o-O=~_o-O=~_o-O=~_o-O=~_o-O=~_o-O=
Those first to step up and say,
"Now is not the time for placing blame"
...
...are quite often to blame....
_o-O=~_o-O=~_o-O=~_o-O=~_o-O=~_o-O=~_o-O=
I think it is quite possible for things to just be and that there
doesn't NEED to be a cause or explanation for everything - it is just
that society (and religion) has conditioned us to think that way.
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| User: "James Ascher" |
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| Title: Re: Why infinity equals zero? |
23 Sep 2005 08:19:47 PM |
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Uncle Buck wrote:
This is a mental game I'm playing at the moment as I dig for deeper
"truths", so please bear with me.
Existence can be defined by innumerable parameters. One of the
parameters - mentioned in the "something from nothing" post - is the
degree of precision necessary for maintaining the existence of
something.
In that post, I noted (in slightly fewer words) the observation that
the more precise a set of parameters must be in order for the
existence of something to be defined, the less stable the existence of
that something becomes as defined by that parameter set.
With regard to the degree of precision necessary to maintain a "True
Nothing" and the degree of precision necessary to maintain a "Truly
Infinite", both are precisely equal. Both "True Nothing" and "Truly
Infinite" are very specific parameter sets, the integrity of which
_any_ deviation obliviates.
Perhaps we've been focussing on the wrong sort of quality when trying
to figure existence out. We look at temperature, mass, volume, etc...
But those things don't really define what is happening so much as they
seem to define the _results_ of what is happening. Is there a set of
cognitive empirical tools one might utilize to study reality more
directly, one that includes such things as "degree of precision
necessary to define the phenomenon in question"? One that seeks to
infer some of the qualitative aspects of existence based upon the
techniques used to observe it?
I know it's not very "scientific" or "detailed", but I think it could
become so. This train of thought is just beginning, after all. With
regard to infinity and zero, might something such as what can be
inferred from the above line of thinking be behind the success of the
practice of "simplification"?
To begin with, this sounds interesting, but the concepts of "zero" and
"infinity" are diametrically opposed. To wit, the concept "zero" is the
idea of nothingness - in math, just a place holder. Even nothingness can
have a function, however - as I understand it, higher maths like
trigonometry and the calculus (to be precise), are impossible without
the concept of "zero".
On the other hand, "infinity" encompasses everything conceivable and
inconceivable at any level of understanding. My limited understanding of
math and its applications informs me that "infinity" in a very useful
concept in specialized applications.
Perhaps the more scientifically or mathematically inclined among us can
explain the implications of "infinity" better.
James
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