| Topic: |
Science > Physics |
| User: |
"Lester Zick" |
| Date: |
13 Mar 2007 12:52:40 PM |
| Object: |
The Definition of Points |
The Definition of Points
~v~~
In the swansong of modern math lines are composed of points. But then
we must ask how points are defined? However I seem to recollect
intersections of lines determine points. But if so then we are left to
consider the rather peculiar proposition that lines are composed of
the intersection of lines. Now I don't claim the foregoing definitions
are circular. Only that the ratio of definitional logic to conclusions
is a transcendental somewhere in the neighborhood of 3.14159 . . .
~v~~
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
29 Mar 2007 05:05:20 PM |
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On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Finite addition never produces infinites in magnitude any more than
bisection produces infinitesimals in magnitude. It's the process which
is infinite or infinitesimal and not the magnitude of results. Results
of infinite addition or infinite bisection are always finite.
Wrong.
Sure I'm wrong, Tony. Because you say so?
Because the results you toe up to only hold in the finite case.
So what's the non finite case? And don't tell me that the non finite
case is infinite because that's redundant and just tells us you claim
there is a non finite case, Tony, and not what it is.
You can
start with 0, or anything in the "finite" arena, the countable
neighborhood around 0, and if you add some infinite value a finite
number of times, or a finite value some infinite number of times, you're
going to get an infinite product. If your set is one of cumulative sets
of increments, like the naturals, then any infinite set is going to
count its way up to infinite values.
Sure. If you have infinites to begin with you'll have infinites to
talk about without having to talk about how the infinites you
have to talk about got to be that way in the first place.
~v~~
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| User: "" |
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| Title: Re: The Definition of Points |
29 Mar 2007 05:56:18 PM |
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Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Finite addition never produces infinites in magnitude any more than
bisection produces infinitesimals in magnitude. It's the process which
is infinite or infinitesimal and not the magnitude of results. Results
of infinite addition or infinite bisection are always finite.
Wrong.
Sure I'm wrong, Tony. Because you say so?
Because the results you toe up to only hold in the finite case.
So what's the non finite case? And don't tell me that the non finite
case is infinite because that's redundant and just tells us you claim
there is a non finite case, Tony, and not what it is.
You can
start with 0, or anything in the "finite" arena, the countable
neighborhood around 0, and if you add some infinite value a finite
number of times, or a finite value some infinite number of times, you're
going to get an infinite product. If your set is one of cumulative sets
of increments, like the naturals, then any infinite set is going to
count its way up to infinite values.
Sure. If you have infinites to begin with you'll have infinites to
talk about without having to talk about how the infinites you
have to talk about got to be that way in the first place.
Confused about absolute infinity? :-)
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
29 Mar 2007 09:26:52 PM |
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On Thu, 29 Mar 2007 16:56:18 -0600, "nonsense@unsettled.com"
<nonsense@unsettled.com> wrote:
Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Finite addition never produces infinites in magnitude any more than
bisection produces infinitesimals in magnitude. It's the process which
is infinite or infinitesimal and not the magnitude of results. Results
of infinite addition or infinite bisection are always finite.
Wrong.
Sure I'm wrong, Tony. Because you say so?
Because the results you toe up to only hold in the finite case.
So what's the non finite case? And don't tell me that the non finite
case is infinite because that's redundant and just tells us you claim
there is a non finite case, Tony, and not what it is.
You can
start with 0, or anything in the "finite" arena, the countable
neighborhood around 0, and if you add some infinite value a finite
number of times, or a finite value some infinite number of times, you're
going to get an infinite product. If your set is one of cumulative sets
of increments, like the naturals, then any infinite set is going to
count its way up to infinite values.
Sure. If you have infinites to begin with you'll have infinites to
talk about without having to talk about how the infinites you
have to talk about got to be that way in the first place.
Confused about absolute infinity? :-)
Someone is.
~v~~
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| User: "Tony Orlow" |
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| Title: Re: The Definition of Points |
30 Mar 2007 12:22:30 PM |
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Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Finite addition never produces infinites in magnitude any more than
bisection produces infinitesimals in magnitude. It's the process which
is infinite or infinitesimal and not the magnitude of results. Results
of infinite addition or infinite bisection are always finite.
Wrong.
Sure I'm wrong, Tony. Because you say so?
Because the results you toe up to only hold in the finite case.
So what's the non finite case? And don't tell me that the non finite
case is infinite because that's redundant and just tells us you claim
there is a non finite case, Tony, and not what it is.
If you define the infinite as any number greater than any finite number,
and you derive an inductive result that, say, f(x)=g(x) for all x
greater than some finite k, well, any infinite x is greater than k, and
so the proof should hold in that infinite case. Where the proof is that
f(x)>g(x), there needs to be further stipulation that lim(x->oo:
f(x)-g(x))>0, otherwise the proof is only valid for the finite case.
That's my rules for infinite-case inductive proof. It's post-Cantorian,
the foundation for IFR and N=S^L. :)
You can
start with 0, or anything in the "finite" arena, the countable
neighborhood around 0, and if you add some infinite value a finite
number of times, or a finite value some infinite number of times, you're
going to get an infinite product. If your set is one of cumulative sets
of increments, like the naturals, then any infinite set is going to
count its way up to infinite values.
Sure. If you have infinites to begin with you'll have infinites to
talk about without having to talk about how the infinites you
have to talk about got to be that way in the first place.
~v~~
Well sure, that's science. Declare a unit, then measure with it and
figure out the rules or measurement, right?
01oo
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
31 Mar 2007 06:55:19 PM |
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On Fri, 30 Mar 2007 12:22:30 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Finite addition never produces infinites in magnitude any more than
bisection produces infinitesimals in magnitude. It's the process which
is infinite or infinitesimal and not the magnitude of results. Results
of infinite addition or infinite bisection are always finite.
Wrong.
Sure I'm wrong, Tony. Because you say so?
Because the results you toe up to only hold in the finite case.
So what's the non finite case? And don't tell me that the non finite
case is infinite because that's redundant and just tells us you claim
there is a non finite case, Tony, and not what it is.
If you define the infinite as any number greater than any finite number,
and you derive an inductive result that, say, f(x)=g(x) for all x
greater than some finite k, well, any infinite x is greater than k, and
so the proof should hold in that infinite case. Where the proof is that
f(x)>g(x), there needs to be further stipulation that lim(x->oo:
f(x)-g(x))>0, otherwise the proof is only valid for the finite case.
That's my rules for infinite-case inductive proof. It's post-Cantorian,
the foundation for IFR and N=S^L. :)
You can
start with 0, or anything in the "finite" arena, the countable
neighborhood around 0, and if you add some infinite value a finite
number of times, or a finite value some infinite number of times, you're
going to get an infinite product. If your set is one of cumulative sets
of increments, like the naturals, then any infinite set is going to
count its way up to infinite values.
Sure. If you have infinites to begin with you'll have infinites to
talk about without having to talk about how the infinites you
have to talk about got to be that way in the first place.
~v~~
Well sure, that's science. Declare a unit, then measure with it and
figure out the rules or measurement, right?
I have no idea what you think science is, Tony. Declare what and then
measure what and figure out the rules of what, right, when you've got
nothing better to do of an afternoon?
~v~~
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| User: "Tony Orlow" |
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| Title: Re: The Definition of Points |
31 Mar 2007 07:50:10 PM |
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Lester Zick wrote:
On Fri, 30 Mar 2007 12:22:30 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Finite addition never produces infinites in magnitude any more than
bisection produces infinitesimals in magnitude. It's the process which
is infinite or infinitesimal and not the magnitude of results. Results
of infinite addition or infinite bisection are always finite.
Wrong.
Sure I'm wrong, Tony. Because you say so?
Because the results you toe up to only hold in the finite case.
So what's the non finite case? And don't tell me that the non finite
case is infinite because that's redundant and just tells us you claim
there is a non finite case, Tony, and not what it is.
If you define the infinite as any number greater than any finite number,
and you derive an inductive result that, say, f(x)=g(x) for all x
greater than some finite k, well, any infinite x is greater than k, and
so the proof should hold in that infinite case. Where the proof is that
f(x)>g(x), there needs to be further stipulation that lim(x->oo:
f(x)-g(x))>0, otherwise the proof is only valid for the finite case.
That's my rules for infinite-case inductive proof. It's post-Cantorian,
the foundation for IFR and N=S^L. :)
You can
start with 0, or anything in the "finite" arena, the countable
neighborhood around 0, and if you add some infinite value a finite
number of times, or a finite value some infinite number of times, you're
going to get an infinite product. If your set is one of cumulative sets
of increments, like the naturals, then any infinite set is going to
count its way up to infinite values.
Sure. If you have infinites to begin with you'll have infinites to
talk about without having to talk about how the infinites you
have to talk about got to be that way in the first place.
~v~~
Well sure, that's science. Declare a unit, then measure with it and
figure out the rules or measurement, right?
I have no idea what you think science is, Tony. Declare what and then
measure what and figure out the rules of what, right, when you've got
nothing better to do of an afternoon?
~v~~
I've been dropping feathers and bowling balls out my window all
morning.... What do YOU think science is?
01oo
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
01 Apr 2007 06:41:35 PM |
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On Sat, 31 Mar 2007 19:50:10 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Fri, 30 Mar 2007 12:22:30 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Finite addition never produces infinites in magnitude any more than
bisection produces infinitesimals in magnitude. It's the process which
is infinite or infinitesimal and not the magnitude of results. Results
of infinite addition or infinite bisection are always finite.
Wrong.
Sure I'm wrong, Tony. Because you say so?
Because the results you toe up to only hold in the finite case.
So what's the non finite case? And don't tell me that the non finite
case is infinite because that's redundant and just tells us you claim
there is a non finite case, Tony, and not what it is.
If you define the infinite as any number greater than any finite number,
and you derive an inductive result that, say, f(x)=g(x) for all x
greater than some finite k, well, any infinite x is greater than k, and
so the proof should hold in that infinite case. Where the proof is that
f(x)>g(x), there needs to be further stipulation that lim(x->oo:
f(x)-g(x))>0, otherwise the proof is only valid for the finite case.
That's my rules for infinite-case inductive proof. It's post-Cantorian,
the foundation for IFR and N=S^L. :)
You can
start with 0, or anything in the "finite" arena, the countable
neighborhood around 0, and if you add some infinite value a finite
number of times, or a finite value some infinite number of times, you're
going to get an infinite product. If your set is one of cumulative sets
of increments, like the naturals, then any infinite set is going to
count its way up to infinite values.
Sure. If you have infinites to begin with you'll have infinites to
talk about without having to talk about how the infinites you
have to talk about got to be that way in the first place.
~v~~
Well sure, that's science. Declare a unit, then measure with it and
figure out the rules or measurement, right?
I have no idea what you think science is, Tony. Declare what and then
measure what and figure out the rules of what, right, when you've got
nothing better to do of an afternoon?
~v~~
I've been dropping feathers and bowling balls out my window all
morning.... What do YOU think science is?
Exactly what I said it was in E201: the demonstration of truth. That
and nothing more or less.
~v~~
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
29 Mar 2007 05:33:53 PM |
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On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
If I don't seem particularly interested in demonstrations of universal
truth it's partly because you aren't doing any and I've already done
the only ones which can matter. It's rather like the problem of 1+1=2
or the rac trisection of general angles. Once demonstrated in reduced
mechanically exhaustive terms the problem if not its explication and
implications loses interest. If you want to argue the problem itself
go ahead. Just don't expect me to be interested in whether 1+1=2 or
whether you can trisect general angles.
You assume OR in defining AND, and then derive OR from AND, all the
while claiming all you've done is NOT.
Of course I do. That's specifically why I chose to specify (A B) so I
could get around the presence of conjunctions like "or" which I didn't
know were there but I'll take your word for it since you seem to know
and say what's there and what's not without having to demonstrate it
whereas I'm forced to demonstrate what I say even though you don't. So
I suppose we can just assume (A B) means there's a conjunction
involved on your per say without having to demonstrate its presence.
~v~~
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| User: "Tony Orlow" |
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| Title: Re: The Definition of Points |
30 Mar 2007 12:33:00 PM |
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Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
If I don't seem particularly interested in demonstrations of universal
truth it's partly because you aren't doing any and I've already done
the only ones which can matter. It's rather like the problem of 1+1=2
or the rac trisection of general angles. Once demonstrated in reduced
mechanically exhaustive terms the problem if not its explication and
implications loses interest. If you want to argue the problem itself
go ahead. Just don't expect me to be interested in whether 1+1=2 or
whether you can trisect general angles.
You assume OR in defining AND, and then derive OR from AND, all the
while claiming all you've done is NOT.
Of course I do. That's specifically why I chose to specify (A B) so I
could get around the presence of conjunctions like "or" which I didn't
know were there but I'll take your word for it since you seem to know
and say what's there and what's not without having to demonstrate it
whereas I'm forced to demonstrate what I say even though you don't. So
I suppose we can just assume (A B) means there's a conjunction
involved on your per say without having to demonstrate its presence.
~v~~
Okay, fill in this table for me please, explaining whether (A B) is true
or false in the following circumstances:
A B (A B)
true true true or false?
true false true or false?
false true true or false?
false false true or false?
Now, we can see what 2-place operator you're talking about.
01oo
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
31 Mar 2007 07:13:55 PM |
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On Fri, 30 Mar 2007 12:33:00 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
If I don't seem particularly interested in demonstrations of universal
truth it's partly because you aren't doing any and I've already done
the only ones which can matter. It's rather like the problem of 1+1=2
or the rac trisection of general angles. Once demonstrated in reduced
mechanically exhaustive terms the problem if not its explication and
implications loses interest. If you want to argue the problem itself
go ahead. Just don't expect me to be interested in whether 1+1=2 or
whether you can trisect general angles.
You assume OR in defining AND, and then derive OR from AND, all the
while claiming all you've done is NOT.
Of course I do. That's specifically why I chose to specify (A B) so I
could get around the presence of conjunctions like "or" which I didn't
know were there but I'll take your word for it since you seem to know
and say what's there and what's not without having to demonstrate it
whereas I'm forced to demonstrate what I say even though you don't. So
I suppose we can just assume (A B) means there's a conjunction
involved on your per say without having to demonstrate its presence.
~v~~
Okay, fill in this table for me please, explaining whether (A B) is true
or false in the following circumstances:
What table, Tony? What true false?
A B (A B)
true true true or false?
true false true or false?
false true true or false?
false false true or false?
Now, we can see what 2-place operator you're talking about.
What two place operator, Tony? Would you care to define any of these
terms before talking about them or should we try to talk about them
before defining them? I don't mind talking about tables, true, false,
two place operators, etc. before defining them but then I insist on my
definitions intead of yours. Of course I can't tell exactly what my
definitions might be until I define them in preference to yours. But
that doesn't really matter since they're my definitions to begin with.
~v~~
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| User: "Tony Orlow" |
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| Title: Re: The Definition of Points |
31 Mar 2007 08:51:49 PM |
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Lester Zick wrote:
On Fri, 30 Mar 2007 12:33:00 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
If I don't seem particularly interested in demonstrations of universal
truth it's partly because you aren't doing any and I've already done
the only ones which can matter. It's rather like the problem of 1+1=2
or the rac trisection of general angles. Once demonstrated in reduced
mechanically exhaustive terms the problem if not its explication and
implications loses interest. If you want to argue the problem itself
go ahead. Just don't expect me to be interested in whether 1+1=2 or
whether you can trisect general angles.
You assume OR in defining AND, and then derive OR from AND, all the
while claiming all you've done is NOT.
Of course I do. That's specifically why I chose to specify (A B) so I
could get around the presence of conjunctions like "or" which I didn't
know were there but I'll take your word for it since you seem to know
and say what's there and what's not without having to demonstrate it
whereas I'm forced to demonstrate what I say even though you don't. So
I suppose we can just assume (A B) means there's a conjunction
involved on your per say without having to demonstrate its presence.
~v~~
Okay, fill in this table for me please, explaining whether (A B) is true
or false in the following circumstances:
What question are you about to ask?
What table, Tony? What true false?
A B (A B)
true true true or false?
true false true or false?
false true true or false?
false false true or false?
Now, we can see what 2-place operator you're talking about.
Okay, now it looks like you changed two of the "true or false?" entries.
No, it's just bad tabbing...
What two place operator, Tony? Would you care to define any of these
terms before talking about them or should we try to talk about them
before defining them? I don't mind talking about tables, true, false,
two place operators, etc. before defining them but then I insist on my
definitions intead of yours. Of course I can't tell exactly what my
definitions might be until I define them in preference to yours. But
that doesn't really matter since they're my definitions to begin with.
~v~~
wahhhh....
sigh.
Okely dokums. Here goes, again.
A logical statement can be classified as true or false? True or false?
A logical operator can be defined as one taking some number of arguments
or parameters, and producing a statement that falls in one class or the
other. True or false?
A statement cannot have a negative number of variables, can it? So, the
fewest parameters it can have is zero, and the only two operators that
put out values of "true" and "false" given no inputs are true() and
false(). There are 2^0=1 inputs, or no choice, and 2^1 outputs, two
possible.
Out of the 1-place operators, there are four. There are 2^1=2 possible
input states, and 2^2=4 possible output mappings. One is always true and
one always false, no matter what the input is, so those are redundant.
Call the input x, either 0 or 1. One of the 1-place operators is the
same as x. The only other of the four is not(x). That'd the only 1-place
operator of any significance.
When it comes to 2-place operators, there's A and B, A or B, A xor B, A
implies B, A is implied by B, and their negations, pretty much.
01oo
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
01 Apr 2007 08:10:10 PM |
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On Sat, 31 Mar 2007 20:51:49 -0500, Tony Orlow <tony@lightlink.com>
wrote:
A logical statement can be classified as true or false? True or false?
You show me the demonstration of your answer, Tony, because it's your
question and your claim not mine.
~v~~
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| User: "Tony Orlow" |
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| Title: Re: The Definition of Points |
12 Apr 2007 01:31:52 PM |
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Lester Zick wrote:
On Sat, 31 Mar 2007 20:51:49 -0500, Tony Orlow <tony@lightlink.com>
wrote:
A logical statement can be classified as true or false? True or false?
You show me the demonstration of your answer, Tony, because it's your
question and your claim not mine.
~v~~
I am asking you whether that statement is true or false. If you have a
third answer, I'll be happy to entertain it.
01oo
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
12 Apr 2007 05:51:25 PM |
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On Thu, 12 Apr 2007 14:31:52 -0400, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Sat, 31 Mar 2007 20:51:49 -0500, Tony Orlow <tony@lightlink.com>
wrote:
A logical statement can be classified as true or false? True or false?
You show me the demonstration of your answer, Tony, because it's your
question and your claim not mine.
~v~~
I am asking you whether that statement is true or false. If you have a
third answer, I'll be happy to entertain it.
The point being, Tony, that you don't have a first answer much less a
second or third. You can't tell me or anyone else what it means to be
true in mechanically exhaustive terms. Mathematikers routinely demand
students deal in the most exacting exhaustive mechanical terms with
axioms, theorems, and doctrines of their own. Yet the moment they're
required to deal with their own axioms, doctrines, and assumptions of
truth in mechanically exhaustive terms they shy away with complaints
no one can expect to prove the truth of what they assume to be true.
You draw up all kinds of binary "truth" tables as if they meant or had
to mean something in mechanically exhaustive terms and demand others
deal with them in binary terms you set forth. Yet you can't explain
what you mean by "truth" or "falsity" in mechanically exhaustive terms
to begin with. So how do you expect anyone to deal with truth tables?
~v~~
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| User: "Tony Orlow" |
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| Title: Re: The Definition of Points |
13 Apr 2007 12:45:46 PM |
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Lester Zick wrote:
On Thu, 12 Apr 2007 14:31:52 -0400, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Sat, 31 Mar 2007 20:51:49 -0500, Tony Orlow <tony@lightlink.com>
wrote:
A logical statement can be classified as true or false? True or false?
You show me the demonstration of your answer, Tony, because it's your
question and your claim not mine.
~v~~
I am asking you whether that statement is true or false. If you have a
third answer, I'll be happy to entertain it.
The point being, Tony, that you don't have a first answer much less a
second or third. You can't tell me or anyone else what it means to be
true in mechanically exhaustive terms. Mathematikers routinely demand
students deal in the most exacting exhaustive mechanical terms with
axioms, theorems, and doctrines of their own. Yet the moment they're
required to deal with their own axioms, doctrines, and assumptions of
truth in mechanically exhaustive terms they shy away with complaints
no one can expect to prove the truth of what they assume to be true.
You draw up all kinds of binary "truth" tables as if they meant or had
to mean something in mechanically exhaustive terms and demand others
deal with them in binary terms you set forth. Yet you can't explain
what you mean by "truth" or "falsity" in mechanically exhaustive terms
to begin with. So how do you expect anyone to deal with truth tables?
~v~~
Just answer the question above.
01oo
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
13 Apr 2007 05:33:27 PM |
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On Fri, 13 Apr 2007 13:45:46 -0400, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Thu, 12 Apr 2007 14:31:52 -0400, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Sat, 31 Mar 2007 20:51:49 -0500, Tony Orlow <tony@lightlink.com>
wrote:
A logical statement can be classified as true or false? True or false?
You show me the demonstration of your answer, Tony, because it's your
question and your claim not mine.
~v~~
I am asking you whether that statement is true or false. If you have a
third answer, I'll be happy to entertain it.
The point being, Tony, that you don't have a first answer much less a
second or third. You can't tell me or anyone else what it means to be
true in mechanically exhaustive terms. Mathematikers routinely demand
students deal in the most exacting exhaustive mechanical terms with
axioms, theorems, and doctrines of their own. Yet the moment they're
required to deal with their own axioms, doctrines, and assumptions of
truth in mechanically exhaustive terms they shy away with complaints
no one can expect to prove the truth of what they assume to be true.
You draw up all kinds of binary "truth" tables as if they meant or had
to mean something in mechanically exhaustive terms and demand others
deal with them in binary terms you set forth. Yet you can't explain
what you mean by "truth" or "falsity" in mechanically exhaustive terms
to begin with. So how do you expect anyone to deal with truth tables?
~v~~
Just answer the question above.
What question? You seem to think there is a question apart from
whether a statement is true or false. All your classifications rely on
that presumption. But you can't tell me what it means to be true or
false so I don't know how to answer the question in terms that will
satisfy you.
~v~~
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| User: "Tony Orlow" |
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| Title: Re: The Definition of Points |
17 Apr 2007 11:20:01 AM |
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Lester Zick wrote:
On Fri, 13 Apr 2007 13:45:46 -0400, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Thu, 12 Apr 2007 14:31:52 -0400, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Sat, 31 Mar 2007 20:51:49 -0500, Tony Orlow <tony@lightlink.com>
wrote:
A logical statement can be classified as true or false? True or false?
You show me the demonstration of your answer, Tony, because it's your
question and your claim not mine.
~v~~
I am asking you whether that statement is true or false. If you have a
third answer, I'll be happy to entertain it.
The point being, Tony, that you don't have a first answer much less a
second or third. You can't tell me or anyone else what it means to be
true in mechanically exhaustive terms. Mathematikers routinely demand
students deal in the most exacting exhaustive mechanical terms with
axioms, theorems, and doctrines of their own. Yet the moment they're
required to deal with their own axioms, doctrines, and assumptions of
truth in mechanically exhaustive terms they shy away with complaints
no one can expect to prove the truth of what they assume to be true.
You draw up all kinds of binary "truth" tables as if they meant or had
to mean something in mechanically exhaustive terms and demand others
deal with them in binary terms you set forth. Yet you can't explain
what you mean by "truth" or "falsity" in mechanically exhaustive terms
to begin with. So how do you expect anyone to deal with truth tables?
~v~~
Just answer the question above.
What question? You seem to think there is a question apart from
whether a statement is true or false. All your classifications rely on
that presumption. But you can't tell me what it means to be true or
false so I don't know how to answer the question in terms that will
satisfy you.
~v~~
A logical statement can be classified as true or false? True or false?
In other words, is there a third option, for this or any other statement?
01oo
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
17 Apr 2007 05:11:48 PM |
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On Tue, 17 Apr 2007 12:20:01 -0400, Tony Orlow <tony@lightlink.com>
wrote:
What question? You seem to think there is a question apart from
whether a statement is true or false. All your classifications rely on
that presumption. But you can't tell me what it means to be true or
false so I don't know how to answer the question in terms that will
satisfy you.
~v~~
A logical statement can be classified as true or false? True or false?
A logical statement as opposed to what, Tony?
In other words, is there a third option, for this or any other statement?
Hard to tell without seeing the statement.
~v~~
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| User: "Tony Orlow" |
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| Title: Re: The Definition of Points |
18 Apr 2007 01:31:35 PM |
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Lester Zick wrote:
On Tue, 17 Apr 2007 12:20:01 -0400, Tony Orlow <tony@lightlink.com>
wrote:
What question? You seem to think there is a question apart from
whether a statement is true or false. All your classifications rely on
that presumption. But you can't tell me what it means to be true or
false so I don't know how to answer the question in terms that will
satisfy you.
~v~~
A logical statement can be classified as true or false? True or false?
A logical statement as opposed to what, Tony?
As opposed to, say, an arithmetic formula.
In other words, is there a third option, for this or any other statement?
Hard to tell without seeing the statement.
~v~~
No, it's up to you. A logical statement is one that has some measure of
truth, from false to true. One can consider just false and true, or one
can consider a multilevel logic like a scale from 1 to 10, or even a
probabilistic logic with all real values from 0 through 1. Since you
only speak of truth versus falsity, I imagine you are considering the
first type, or Boolean binary logic.
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
18 Apr 2007 06:42:19 PM |
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On Wed, 18 Apr 2007 14:31:35 -0400, Tony Orlow <tony@lightlink.com>
wrote:
Lester Zick wrote:
On Tue, 17 Apr 2007 12:20:01 -0400, Tony Orlow <tony@lightlink.com>
wrote:
What question? You seem to think there is a question apart from
whether a statement is true or false. All your classifications rely on
that presumption. But you can't tell me what it means to be true or
false so I don't know how to answer the question in terms that will
satisfy you.
~v~~
A logical statement can be classified as true or false? True or false?
A logical statement as opposed to what, Tony?
As opposed to, say, an arithmetic formula.
So arithmetic formulas are not logical?
In other words, is there a third option, for this or any other statement?
Hard to tell without seeing the statement.
~v~~
No, it's up to you.
Good. The logical statement "it is black" is true.
A logical statement is one that has some measure of
truth, from false to true. One can consider just false and true, or one
can consider a multilevel logic like a scale from 1 to 10, or even a
probabilistic logic with all real values from 0 through 1. Since you
only speak of truth versus falsity, I imagine you are considering the
first type, or Boolean binary logic.
So "black is crow" is either true or false? Or is not a logical
statement? 'Fraid you'll just have to help me out here, Tony. Just
tell me what you want me to say.
~v~~
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
29 Mar 2007 04:56:38 PM |
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On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
In other words modern mathematikers just assume that because the Peano
and suc( ) axioms produce successive straight line segments between
numbers there is some kind of guarantee that the successive straight
line segments will themselves line up colinearly on straight line
segments and that we can thus just assume or infer the existence of
straight line segments and straight lines from those axioms.Doesn't
happen that way because even if we assume the existence of straight
line segments between numbers that doesn't demand successive segments
align in any particular direction colinearly along any common straight
line segment. Same principle as above, different application.
"Straight" doesn't even seem to mean anything in the context of Peano...
"Straight" certainly seems to mean something to mathematikers who talk
about straight lines and geometry.
~v~~
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
29 Mar 2007 04:49:41 PM |
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On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
It's modern mathematikers and empirics who ask gods for revelations. I
concentrate on demonstrating what's true and false in mechanically
reduced exhaustive terms of finite tautological regression to self
contradictory alternatives. Whole nuther kettle of fish.
Smells a little familiar...
Only because you're used to the smell of something rotten in the state
of Denmark.
~v~~
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
29 Mar 2007 05:12:54 PM |
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On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Just ask yourself, Tony, at what magic point do intervals become
infinitesimal instead of finite? Your answer should be magnitudes
become infintesimal when subdivision becomes infinite.
Yes.
Yes but that doesn't happen until intervals actually become zero.
But the term
"infinite" just means undefined and in point of fact doesn't become
infinite until intervals become zero in magnitude. But that never
happens.
But, but, but. No, "infinite" means "greater than any finite number" and
infinitesimal means "less than any finite number", where "less" means
"closer to 0" and "more" means "farther from 0".
Problem is you can't say when that is in terms of infinite bisection.
~v~~
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| User: "Tony Orlow" |
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| Title: Re: The Definition of Points |
30 Mar 2007 12:27:40 PM |
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Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Just ask yourself, Tony, at what magic point do intervals become
infinitesimal instead of finite? Your answer should be magnitudes
become infintesimal when subdivision becomes infinite.
Yes.
Yes but that doesn't happen until intervals actually become zero.
But the term
"infinite" just means undefined and in point of fact doesn't become
infinite until intervals become zero in magnitude. But that never
happens.
But, but, but. No, "infinite" means "greater than any finite number" and
infinitesimal means "less than any finite number", where "less" means
"closer to 0" and "more" means "farther from 0".
Problem is you can't say when that is in terms of infinite bisection.
~v~~
Cantorians try with their lame "aleph_0". Better you get used to the
fact that there is no more a smallest infinity than a smallest finite,
largest finite, or smallest or largest infinitesimal. Those things
simply don't exist, except as phantoms.
01oo
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| User: "Virgil" |
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| Title: Re: The Definition of Points |
30 Mar 2007 01:31:08 PM |
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In article <460d489b@news2.lightlink.com>,
Tony Orlow <tony@lightlink.com> wrote:
Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Just ask yourself, Tony, at what magic point do intervals become
infinitesimal instead of finite? Your answer should be magnitudes
become infintesimal when subdivision becomes infinite.
Yes.
Yes but that doesn't happen until intervals actually become zero.
But the term
"infinite" just means undefined and in point of fact doesn't become
infinite until intervals become zero in magnitude. But that never
happens.
But, but, but. No, "infinite" means "greater than any finite number" and
infinitesimal means "less than any finite number", where "less" means
"closer to 0" and "more" means "farther from 0".
Problem is you can't say when that is in terms of infinite bisection.
~v~~
Cantorians try with their lame "aleph_0". Better you get used to the
fact that there is no more a smallest infinity than a smallest finite,
largest finite, or smallest or largest infinitesimal. Those things
simply don't exist, except as phantoms.
But all other mathematical objects are equally fantastic, having no
physical reality, but existing only in the imagination. So any statement
of mathematical existence is always relative to something like a system
of axioms.
.
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| User: "Lester Zick" |
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| Title: Re: The Definition of Points |
31 Mar 2007 07:06:44 PM |
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On Fri, 30 Mar 2007 12:31:08 -0600, Virgil <virgil@comcast.net> wrote:
In article <460d489b@news2.lightlink.com>,
Tony Orlow <tony@lightlink.com> wrote:
Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Just ask yourself, Tony, at what magic point do intervals become
infinitesimal instead of finite? Your answer should be magnitudes
become infintesimal when subdivision becomes infinite.
Yes.
Yes but that doesn't happen until intervals actually become zero.
But the term
"infinite" just means undefined and in point of fact doesn't become
infinite until intervals become zero in magnitude. But that never
happens.
But, but, but. No, "infinite" means "greater than any finite number" and
infinitesimal means "less than any finite number", where "less" means
"closer to 0" and "more" means "farther from 0".
Problem is you can't say when that is in terms of infinite bisection.
~v~~
Cantorians try with their lame "aleph_0". Better you get used to the
fact that there is no more a smallest infinity than a smallest finite,
largest finite, or smallest or largest infinitesimal. Those things
simply don't exist, except as phantoms.
But all other mathematical objects are equally fantastic, having no
physical reality, but existing only in the imagination. So any statement
of mathematical existence is always relative to something like a system
of axioms.
Whew. Means you don't have to consider whether they're true. Quite
a relief I'd say. You can always take it up with someone who unlike
yourself isn't too lazy or stupid to think for a living.
~v~~
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| User: "Tony Orlow" |
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| Title: Re: The Definition of Points |
31 Mar 2007 08:23:35 PM |
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Lester Zick wrote:
On Fri, 30 Mar 2007 12:31:08 -0600, Virgil <virgil@comcast.net> wrote:
In article <460d489b@news2.lightlink.com>,
Tony Orlow <tony@lightlink.com> wrote:
Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Just ask yourself, Tony, at what magic point do intervals become
infinitesimal instead of finite? Your answer should be magnitudes
become infintesimal when subdivision becomes infinite.
Yes.
Yes but that doesn't happen until intervals actually become zero.
But the term
"infinite" just means undefined and in point of fact doesn't become
infinite until intervals become zero in magnitude. But that never
happens.
But, but, but. No, "infinite" means "greater than any finite number" and
infinitesimal means "less than any finite number", where "less" means
"closer to 0" and "more" means "farther from 0".
Problem is you can't say when that is in terms of infinite bisection.
~v~~
Cantorians try with their lame "aleph_0". Better you get used to the
fact that there is no more a smallest infinity than a smallest finite,
largest finite, or smallest or largest infinitesimal. Those things
simply don't exist, except as phantoms.
But all other mathematical objects are equally fantastic, having no
physical reality, but existing only in the imagination. So any statement
of mathematical existence is always relative to something like a system
of axioms.
Whew. Means you don't have to consider whether they're true. Quite
a relief I'd say. You can always take it up with someone who unlike
yourself isn't too lazy or stupid to think for a living.
~v~~
Oh, c'mon, Lester. If Virgie says it exists, why question it? He says 0
(zero) exists. I agree. 1 exists too. R exists, and N too, and |N|<|R|,
and N "subset" R too. And 0eN and 1eN, so 0eR and 1eR. Also, 0<1. And if
xeR and zeR and x<z, then E yeR such that x<y and y<z, kinda like 1/2
between 0 and 1. xeN and yeN -> x/yeQ, i.e. 1/2eQ. Seems that |N|<|Q|,
since definitely N is a proper subset of Q. That's not what standard
math tells us, given "cardinality", but we don't have to toe the line,
but it is interesting to consider pi and e and other transcendentals and
their place on the line. Can such a point be "pointed out"?
And if we want to get all standardly stickly about it, x<y -> ~y<x. So,
ain't no circles, and can't that |R|<|N|. Whew! That was close! :)
But, questions remain. Really, when it comes to math, "in my book", it
means methods of calculation, ways of figgerin'. When that addresses
endlessnesses, one can't pretend with integrity to measure something
endless, except as some formulaic expression of progress on the way
"there". These are formulaic expressions.That's IFR and N=S^L.
My friend, points do integrate into lines, according to the dimension
over which they are integrated...
Your intuition is not incorrect regarding the dependency of more limited
dimensions on those more numerous, or even infinite, but that's a
physical creation truth, not a mathematical one, based on waves. Some
things need to be separated, from where I sit. But, this chair is
getting comfortable...still I should go see what the sky is doing...
01oo
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| User: "Tony Orlow" |
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| Title: Re: The Definition of Points |
31 Mar 2007 07:39:48 AM |
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Virgil wrote:
In article <460d489b@news2.lightlink.com>,
Tony Orlow <tony@lightlink.com> wrote:
Lester Zick wrote:
On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony@lightlink.com>
wrote:
Just ask yourself, Tony, at what magic point do intervals become
infinitesimal instead of finite? Your answer should be magnitudes
become infintesimal when subdivision becomes infinite.
Yes.
Yes but that doesn't happen until intervals actually become zero.
But the term
"infinite" just means undefined and in point of fact doesn't become
infinite until intervals become zero in magnitude. But that never
happens.
But, but, but. No, "infinite" means "greater than any finite number" and
infinitesimal means "less than any finite number", where "less" means
"closer to 0" and "more" means "farther from 0".
Problem is you can't say when that is in terms of infinite bisection.
~v~~
Cantorians try with their lame "aleph_0". Better you get used to the
fact that there is no more a smallest infinity than a smallest finite,
largest finite, or smallest or largest infinitesimal. Those things
simply don't exist, except as phantoms.
But all other mathematical objects are equally fantastic, having no
physical reality, but existing only in the imagination. So any statement
of mathematical existence is always relative to something like a system
of axioms.
Sure, but the question is whether any such assumption of existence
introduces nonsense into your system. With the very basic assumption
that subtracting a positive amount from anything makes it less, the
inductive logic that proves there is no largest finite can be applied to
prove there is no smallest infinite:
Assume we are working with positive numbers. Subtract a finite number
from an infinite number. The result must be an infinite number, because
if it were finite, then its addition to the finite number we subtracted
would not yield the original infinite number. The result must be smaller
than the original infinite number, because we have subtracted a positive
amount from it. Therefore, for any infinite number, one can produce a
smaller infinite number, and there is thus no smallest infinite number.
In order to support the notion of aleph_0, one has to discard the basic
notion of subtraction in the infinite case. That seems like an undue
sacrifice to me, for the sake of nonsense. Sorry.
Tony
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| User: "Virgil" |
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| Title: Re: The Definition of Points |
31 Mar 2007 01:54:24 PM |
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In article <460e56a5@news2.lightlink.com>,
Tony Orlow <tony@lightlink.com> wrote:
Virgil wrote:
But all other mathematical objects are equally fantastic, having no
physical reality, but existing only in the imagination. So any statement
of mathematical existence is always relative to something like a system
of axioms.
Sure, but the question is whether any such assumption of existence
introduces nonsense into your system.
It has in each of TO's suggested systems so far.
With the very basic assumption
that subtracting a positive amount from anything makes it less
That presumes at least a definition of "positive" and a definition of
"amount" and a definition of "subtraction" and a definition of "less"
before it makes any sense at all.
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| User: "Tony Orlow" |
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| Title: Re: The Definition of Points |
31 Mar 2007 06:04:27 PM |
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Virgil wrote:
In article <460e56a5@news2.lightlink.com>,
Tony Orlow <tony@lightlink.com> wrote:
Virgil wrote:
But all other mathematical objects are equally fantastic, having no
physical reality, but existing only in the imagination. So any statement
of mathematical existence is always relative to something like a system
of axioms.
Sure, but the question is whether any such assumption of existence
introduces nonsense into your system.
It has in each of TO's suggested systems so far.
If thou so sayest, Sire.
With the very basic assumption
that subtracting a positive amount from anything makes it less
That presumes at least a definition of "positive" and a definition of
"amount" and a definition of "subtraction" and a definition of "less"
before it makes any sense at all.
Yes, it does. I think we all know basically what those terms mean. But,
let's say we don't. We have a system where x<y and y<z implies x<z. We
define 0, and say if x<0, then y+x<y, and if x>0 then y+x>y, and of
course, if x=0, then y+x=y. y+x=z <-> z-y=x and z-x=y. x<y means y is in
the "positive" direction from x. x is the distance from 0, positive if
to the right of 0, negative if to the left, and we move that distance in
the opposite direction from any point to subtract x from it, and
determine the poit indicating the result. If we start at one point, and
move a nonzero distance, do we not end up on another point, different
from the first?
Tony
(I notice you never sign your posts, so, while I kind of like to mirror
the signing styles of various posters in my responses, with you, I got
nuthin' to work with. So, I'll just sign, Tony, and then maybe, you'll
start signing, Evrett, or whatever your name "actually" is. :))
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