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The Ghost In The Machine
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 Posted: Tue Jul 06, 2004 8:36 pm Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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In sci.math, Garry Denke
<garrydenke@usa.com>
wrote
on 6 Jul 2004 02:52:17 -0700
<96f81cbe.0407060152.1896e7b5@posting.google.com>:
| Quote: | The Ghost In The Machine <ewill@aurigae.athghost7038suus.net> wrote in message news:<m1cor1-ffp.ln1@lexi2.athghost7038suus.net>...
In sci.logic, Garry Denke
garrydenke@usa.com
wrote
on 5 Jul 2004 03:11:28 -0700
96f81cbe.0407050211.287338a6@posting.google.com>:
Hello to The Ghost In The Machine,
If the number d equals the number 0 , and the number + equals the
number 0 , then the number - equals the number 0 , under your logic,
and still, d / d makes no sense, and 0 / 0 makes no sense. So what we
need is a consistent set of rules for the three numbers...
0/0 never did make sense. Neither does d = + or -d = -.
Therein the reason we need the number 0 rule, and the number - rule,
and the number + rule.
|
Only if we have all three numbers. Since 0 = + and 0 = -, there's
no real need for the other two.
[snip for brevity]
| Quote: | Any ideas?
Yes. Equate d = 0 and be done with it. This also means, of course,
that 0.999... = 1 - d = 1 = 1.000... , which makes most
number-theoreticians happy. :-)
Pretend the 4th fireworks don't exist?
4a) 0 / 0 = 0
4b) 0 / 0 = 1
4c) 0 / 0 = (the Straight line above)
Is The Ghost In The Machine serious?
|
4d) 0 / 0 = undefined/error/incorrect arithmetical op/exception
[rest snipped]
--
#191, ewill3@earthlink.net
It's still legal to go .sigless. |
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|-|erc
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| Posted: Mon Jul 12, 2004 4:40 am Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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"The Ghost In The Machine" <ewill@aurigae.athghost7038suus.net> wrote
| Quote: | Therein the reason we need the number 0 rule, and the number - rule,
and the number + rule.
Only if we have all three numbers. Since 0 = + and 0 = -, there's
no real need for the other two.
|
Repeatedly toss a coin (infintie times)
What is the probability of HHHHHHHHHHHHHH.... ?
# desired outcomes 1
_____________________ = __________________________
# total outcomes # total outcomes
as total outcomes -> oo, P(H..) > 0
It CAN happen, so the probability is NOT 0.
Herc |
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Martin Shobe
Guest
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| Posted: Mon Jul 12, 2004 8:53 am Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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On Sun, 11 Jul 2004 23:40:39 GMT, "|-|erc" <gotch@beauty.com> wrote:
| Quote: | "The Ghost In The Machine" <ewill@aurigae.athghost7038suus.net> wrote
Therein the reason we need the number 0 rule, and the number - rule,
and the number + rule.
Only if we have all three numbers. Since 0 = + and 0 = -, there's
no real need for the other two.
Repeatedly toss a coin (infintie times)
What is the probability of HHHHHHHHHHHHHH.... ?
# desired outcomes 1
_____________________ = __________________________
# total outcomes # total outcomes
as total outcomes -> oo, P(H..) > 0
It CAN happen, so the probability is NOT 0.
|
Nope. It's 0, for the same reason your SetMinus({.3, .33, .333, ...},
1/3) is 0.
Martin |
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|-|erc
Guest
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| Posted: Mon Jul 12, 2004 9:52 am Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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"Martin Shobe" <mshobe@sbcglobal.net> wrote in
| Quote: | On Sun, 11 Jul 2004 23:40:39 GMT, "|-|erc" <gotch@beauty.com> wrote:
"The Ghost In The Machine" <ewill@aurigae.athghost7038suus.net> wrote
Therein the reason we need the number 0 rule, and the number - rule,
and the number + rule.
Only if we have all three numbers. Since 0 = + and 0 = -, there's
no real need for the other two.
Repeatedly toss a coin (infintie times)
What is the probability of HHHHHHHHHHHHHH.... ?
# desired outcomes 1
_____________________ = __________________________
# total outcomes # total outcomes
as total outcomes -> oo, P(H..) > 0
It CAN happen, so the probability is NOT 0.
Nope. It's 0, for the same reason your SetMinus({.3, .33, .333, ...},
1/3) is 0.
|
HAHAHA now we're splitting hairs. I'm already up to defining aleph+1
as +/oo. Its REALLY SMALL. Its so small you multiply by infinity and only get +.
Herc |
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Barb Knox
Guest
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| Posted: Mon Jul 12, 2004 10:20 am Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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In article <jOoIc.90499$sj4.59583@news-server.bigpond.net.au>,
"|-|erc" <gotch@beauty.com> wrote:
| Quote: | "Martin Shobe" <mshobe@sbcglobal.net> wrote in
On Sun, 11 Jul 2004 23:40:39 GMT, "|-|erc" <gotch@beauty.com> wrote:
"The Ghost In The Machine" <ewill@aurigae.athghost7038suus.net> wrote
Therein the reason we need the number 0 rule, and the number - rule,
and the number + rule.
Only if we have all three numbers. Since 0 = + and 0 = -, there's
no real need for the other two.
Repeatedly toss a coin (infintie times)
What is the probability of HHHHHHHHHHHHHH.... ?
# desired outcomes 1
_____________________ = __________________________
# total outcomes # total outcomes
as total outcomes -> oo, P(H..) > 0
It CAN happen, so the probability is NOT 0.
|
No, as I pointed out to you before, if it happens a *finite* number of times
out of an infinite set of trials then the probability is exactly 0.
| Quote: | Nope. It's 0, for the same reason your SetMinus({.3, .33, .333, ...},
1/3) is 0.
HAHAHA now we're splitting hairs. I'm already up to defining aleph+1
as +/oo. Its REALLY SMALL. Its so small you multiply by infinity and only
get +.
|
Too bad you're not allowed to do that. A PROBABILITY is a REAL number between
0.0 and 1.0 inclusive. Suppose the probability of every infinite sequence of
(mixed) Hs and Ts is some real number epsilon > 0. So if you have more than
(1/epsilon)+1 such sequences then their total probability would be > 1, which
is impossible. But of course there is an infinite set of such sequences,
which is thus more than (1/epsilon)+1 for any epsilon. Therefore, there is no
such epsilon > 0, therefore the probability = 0.
(I hope that, unlike Peter Olcott, you do not object to indirect proofs in
general.)
As I pointed out before, the probability of any particular infinite sequence
(WLOG, a sequence of all Hs) can be seen to be exactly zero by the following
argument:
It would require an infinite tail of Hs, which is the same as having *no* Ts
after some point, which has probability 0.
--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb |
| B B a a r b b |
| BBB aa a r bbb |
----------------------------- |
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|-|erc
Guest
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| Posted: Mon Jul 12, 2004 10:49 am Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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"Barb Knox" <see@sig.below> wrote in
| Quote: | Therein the reason we need the number 0 rule, and the number - rule,
and the number + rule.
Only if we have all three numbers. Since 0 = + and 0 = -, there's
no real need for the other two.
Repeatedly toss a coin (infintie times)
What is the probability of HHHHHHHHHHHHHH.... ?
# desired outcomes 1
_____________________ = __________________________
# total outcomes # total outcomes
as total outcomes -> oo, P(H..) > 0
It CAN happen, so the probability is NOT 0.
No, as I pointed out to you before, if it happens a *finite* number of times
out of an infinite set of trials then the probability is exactly 0.
Nope. It's 0, for the same reason your SetMinus({.3, .33, .333, ...},
1/3) is 0.
HAHAHA now we're splitting hairs. I'm already up to defining aleph+1
as +/oo. Its REALLY SMALL. Its so small you multiply by infinity and only
get +.
Too bad you're not allowed to do that. A PROBABILITY is a REAL number between
0.0 and 1.0 inclusive. Suppose the probability of every infinite sequence of
(mixed) Hs and Ts is some real number epsilon > 0. So if you have more than
(1/epsilon)+1 such sequences then their total probability would be > 1, which
is impossible. But of course there is an infinite set of such sequences,
which is thus more than (1/epsilon)+1 for any epsilon. Therefore, there is no
such epsilon > 0, therefore the probability = 0.
(I hope that, unlike Peter Olcott, you do not object to indirect proofs in
general.)
As I pointed out before, the probability of any particular infinite sequence
(WLOG, a sequence of all Hs) can be seen to be exactly zero by the following
argument:
It would require an infinite tail of Hs, which is the same as having *no* Ts
after some point, which has probability 0.
|
No. Probability = 0 means impossible. some infinite sequence is possible (in the model).
As #trials approaches infinity, the probability approaches 0+.
Or does 1/oo = 0 now?
Herc |
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The Ghost In The Machine
Guest
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| Posted: Mon Jul 12, 2004 1:01 pm Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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In sci.logic, |-|erc
<gotch@beauty.com>
wrote
on Sun, 11 Jul 2004 23:40:39 GMT
<XdkIc.90276$sj4.9495@news-server.bigpond.net.au>:
| Quote: | "The Ghost In The Machine" <ewill@aurigae.athghost7038suus.net> wrote
Therein the reason we need the number 0 rule, and the number - rule,
and the number + rule.
Only if we have all three numbers. Since 0 = + and 0 = -, there's
no real need for the other two.
Repeatedly toss a coin (infintie times)
What is the probability of HHHHHHHHHHHHHH.... ?
|
The same as the probability of TTTTTTTTTT.....or HTHTHTHTHTHTHT....
| Quote: |
# desired outcomes 1
_____________________ = __________________________
# total outcomes # total outcomes
as total outcomes -> oo, P(H..) > 0
It CAN happen, so the probability is NOT 0.
|
I'm not entirely certain as to how one can approach this issue,
as it's clear that oo/oo suffers from the same problem as 0/0;
namely, it's not defined. 1/oo is typically called 0 but there
are problems here, too, as any sequence tending to infinity
is such that the derived sequence of reciprocals are nonzero
(assuming that none of the terms of the original sequence is 0).
However, most people aren't too concerned.
Unfortunately lim (n->oo) P(H...) = 0 anyway, though for any n,
P(H...H) > 0. To claim otherwise leads one into "Garry Denke"
math.
--
#191, ewill3@earthlink.net
It's still legal to go .sigless. |
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|-|erc
Guest
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| Posted: Mon Jul 12, 2004 3:15 pm Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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"The Ghost In The Machine" <ewill@aurigae.athghost7038suus.net> wrote
| Quote: | Therein the reason we need the number 0 rule, and the number - rule,
and the number + rule.
Only if we have all three numbers. Since 0 = + and 0 = -, there's
no real need for the other two.
Repeatedly toss a coin (infintie times)
What is the probability of HHHHHHHHHHHHHH.... ?
The same as the probability of TTTTTTTTTT.....or HTHTHTHTHTHTHT....
# desired outcomes 1
_____________________ = __________________________
# total outcomes # total outcomes
as total outcomes -> oo, P(H..) > 0
It CAN happen, so the probability is NOT 0.
I'm not entirely certain as to how one can approach this issue,
as it's clear that oo/oo suffers from the same problem as 0/0;
namely, it's not defined. 1/oo is typically called 0 but there
are problems here, too, as any sequence tending to infinity
is such that the derived sequence of reciprocals are nonzero
(assuming that none of the terms of the original sequence is 0).
However, most people aren't too concerned.
Unfortunately lim (n->oo) P(H...) = 0 anyway, though for any n,
P(H...H) > 0. To claim otherwise leads one into "Garry Denke"
math.
|
an interesting excursion, we look at [lower 0s] and everyone has to reverse their arguments
from [higher oo's].
| Quote: | Unfortunately lim(n->oo) P(H...) = 0
|
That's just shorthand for n->oo P(H..)->0.
Which is also written
lim(n->oo) P(H..)->0+
as n approaches infinity P approaches 0 from above.
Probability is just a model. [At the limit P=0] does not mean impossible, for obvious reasons.
Herc |
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Barb Knox
Guest
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| Posted: Mon Jul 12, 2004 4:54 pm Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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In article <%DpIc.90532$sj4.31189@news-server.bigpond.net.au>,
"|-|erc" <gotch@beauty.com> wrote:
| Quote: | "Barb Knox" <see@sig.below> wrote in
Therein the reason we need the number 0 rule, and the number - rule,
and the number + rule.
Only if we have all three numbers. Since 0 = + and 0 = -, there's
no real need for the other two.
Repeatedly toss a coin (infintie times)
What is the probability of HHHHHHHHHHHHHH.... ?
# desired outcomes 1
_____________________ = __________________________
# total outcomes # total outcomes
as total outcomes -> oo, P(H..) > 0
It CAN happen, so the probability is NOT 0.
No, as I pointed out to you before, if it happens a *finite* number of times
out of an infinite set of trials then the probability is exactly 0.
Nope. It's 0, for the same reason your SetMinus({.3, .33, .333, ...},
1/3) is 0.
HAHAHA now we're splitting hairs. I'm already up to defining aleph+1
as +/oo. Its REALLY SMALL. Its so small you multiply by infinity and only
get +.
Too bad you're not allowed to do that. A PROBABILITY is a REAL number
between
0.0 and 1.0 inclusive. Suppose the probability of every infinite sequence
of
(mixed) Hs and Ts is some real number epsilon > 0. So if you have more than
(1/epsilon)+1 such sequences then their total probability would be > 1,
which
is impossible. But of course there is an infinite set of such sequences,
which is thus more than (1/epsilon)+1 for any epsilon. Therefore, there is
no
such epsilon > 0, therefore the probability = 0.
(I hope that, unlike Peter Olcott, you do not object to indirect proofs in
general.)
As I pointed out before, the probability of any particular infinite sequence
(WLOG, a sequence of all Hs) can be seen to be exactly zero by the following
argument:
It would require an infinite tail of Hs, which is the same as having *no* Ts
after some point, which has probability 0.
No. Probability = 0 means impossible.
|
No it doesn't, at least not in a mathematical context. (Maybe in a courtroom
it does.)
| Quote: | some infinite sequence is possible (in the model).
As #trials approaches infinity, the probability approaches 0+.
|
That's actually true. And at that limit, 0+ is identically 0.
| Quote: | Or does 1/oo = 0 now?
|
It certainly does. For example, have a look at
<http://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html>, item (7).
Didn't you already know that?
--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb |
| B B a a r b b |
| BBB aa a r bbb |
----------------------------- |
|
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|-|erc
Guest
|
| Posted: Mon Jul 12, 2004 5:20 pm Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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"Barb Knox" <see@sig.below> wrote in
| Quote: | "|-|erc" <gotch@beauty.com> wrote:
"Barb Knox" <see@sig.below> wrote in
Therein the reason we need the number 0 rule, and the number - rule,
and the number + rule.
Only if we have all three numbers. Since 0 = + and 0 = -, there's
no real need for the other two.
Repeatedly toss a coin (infintie times)
What is the probability of HHHHHHHHHHHHHH.... ?
# desired outcomes 1
_____________________ = __________________________
# total outcomes # total outcomes
as total outcomes -> oo, P(H..) > 0
It CAN happen, so the probability is NOT 0.
No, as I pointed out to you before, if it happens a *finite* number of times
out of an infinite set of trials then the probability is exactly 0.
Nope. It's 0, for the same reason your SetMinus({.3, .33, .333, ...},
1/3) is 0.
HAHAHA now we're splitting hairs. I'm already up to defining aleph+1
as +/oo. Its REALLY SMALL. Its so small you multiply by infinity and only
get +.
Too bad you're not allowed to do that. A PROBABILITY is a REAL number
between
0.0 and 1.0 inclusive. Suppose the probability of every infinite sequence
of
(mixed) Hs and Ts is some real number epsilon > 0. So if you have more than
(1/epsilon)+1 such sequences then their total probability would be > 1,
which
is impossible. But of course there is an infinite set of such sequences,
which is thus more than (1/epsilon)+1 for any epsilon. Therefore, there is
no
such epsilon > 0, therefore the probability = 0.
(I hope that, unlike Peter Olcott, you do not object to indirect proofs in
general.)
As I pointed out before, the probability of any particular infinite sequence
(WLOG, a sequence of all Hs) can be seen to be exactly zero by the following
argument:
It would require an infinite tail of Hs, which is the same as having *no* Ts
after some point, which has probability 0.
No. Probability = 0 means impossible.
No it doesn't, at least not in a mathematical context. (Maybe in a courtroom
it does.)
|
Did you or did you not state the following? ;)
But notice the qualification "finite": an *infinite* sequence of Hs has
probability 0, since that would require an infinite tail of Hs, which is the
same as having *no* Ts after some point, which has probability 0.
reads as: H.. is possible, since !T... is possible. big deal
You can see why I introduce basic examples to pin your meaning.
| Quote: | fun coin()
while true
if rnd>0.5 return
wend
for any number of cycles it wont necessarily halt in that time.
for infinite number of cycles there is still one possible outcome, [low, low,
low...] that
shows its impossible to prove that it halts.
It halts with probability 1 (assuming that rnd() uses some truly random
quantum process and not a deterministic pseudo-random generator). That can be
viewed as meaning that it's allowed to fail to halt on a finite number of runs
during an unlimited number of runs of the program. But this is entirely aside
from the argument I've given you to address (twice, so far).
|
Herc : its impossible to prove that it halts
Barb : it halts with P=1
are you agreeing or disagreeing here?
| Quote: |
some infinite sequence is possible (in the model).
As #trials approaches infinity, the probability approaches 0+.
That's actually true. And at that limit, 0+ is identically 0.
|
That's nonsense. At the limit there are oo combinations and P is undefined.
| Quote: |
Or does 1/oo = 0 now?
It certainly does. For example, have a look at
http://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html>, item (7).
Didn't you already know that?
|
"these improper elements are not real numbers, and that this system of extended real numbers is not a field."
how much mickey mouse maths do you have to use to support Cantors bogus idiocy?
9 months examining all these avenues. I have to sum up, getting recognition in Maths
is not an avenue to afford shelter from the Truman Satellite.
xxx
xxx
xxx
yyy is missing
xxx
yxx
yyx
....
look infinity of infinities because yyy is nowhere, open your eyes
Herc |
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Guest
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| Posted: Mon Jul 12, 2004 7:20 pm Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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|-|erc wrote:
| Quote: | "Barb Knox" <see@sig.below> wrote in
Too bad you're not allowed to do that. A PROBABILITY is a REAL number
between
0.0 and 1.0 inclusive. Suppose the probability of every infinite
sequence of
(mixed) Hs and Ts is some real number epsilon > 0. So if you have
more than
(1/epsilon)+1 such sequences then their total probability would be
1, which
is impossible. But of course there is an infinite set of such
sequences,
which is thus more than (1/epsilon)+1 for any epsilon. Therefore,
there is no
such epsilon > 0, therefore the probability = 0.
(I hope that, unlike Peter Olcott, you do not object to indirect
proofs in
general.)
As I pointed out before, the probability of any particular infinite
sequence
(WLOG, a sequence of all Hs) can be seen to be exactly zero by the
following
argument:
It would require an infinite tail of Hs, which is the same as having
*no* Ts
after some point, which has probability 0.
No. Probability = 0 means impossible. some infinite sequence is
possible (in the model).
As #trials approaches infinity, the probability approaches 0+.
|
The problem here is a double definition.
"Impossibility" has been defined simultaneously
as "having probability zero", and as meaning
that something cannot happen.
I am not a lawyer. I do not even see email sent to this address, due to
past DOS attacks. If you wish to respond, do so through this newsgroup. |
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Barb Knox
Guest
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| Posted: Tue Jul 13, 2004 4:40 am Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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In article <pmvIc.90944$sj4.7357@news-server.bigpond.net.au>,
"_|erc" <gotch@beauty.com> wrote:
| Quote: | "Barb Knox" <see@sig.below> wrote in
"_|erc" <gotch@beauty.com> wrote:
"Barb Knox" <see@sig.below> wrote in
Therein the reason we need the number 0 rule, and the number -
rule,
and the number + rule.
Only if we have all three numbers. Since 0 = + and 0 = -, there's
no real need for the other two.
Repeatedly toss a coin (infintie times)
What is the probability of HHHHHHHHHHHHHH.... ?
# desired outcomes 1
_____________________ = __________________________
# total outcomes # total outcomes
as total outcomes -> oo, P(H..) > 0
It CAN happen, so the probability is NOT 0.
No, as I pointed out to you before, if it happens a *finite* number of
times
out of an infinite set of trials then the probability is exactly 0.
Nope. It's 0, for the same reason your SetMinus({.3, .33, .333, ...},
1/3) is 0.
HAHAHA now we're splitting hairs. I'm already up to defining aleph+1
as +/oo. Its REALLY SMALL. Its so small you multiply by infinity and
only
get +.
Too bad you're not allowed to do that. A PROBABILITY is a REAL number
between
0.0 and 1.0 inclusive. Suppose the probability of every infinite
sequence
of
(mixed) Hs and Ts is some real number epsilon > 0. So if you have more
than
(1/epsilon)+1 such sequences then their total probability would be > 1,
which
is impossible. But of course there is an infinite set of such sequences,
which is thus more than (1/epsilon)+1 for any epsilon. Therefore, there
is
no
such epsilon > 0, therefore the probability = 0.
(I hope that, unlike Peter Olcott, you do not object to indirect proofs
in
general.)
As I pointed out before, the probability of any particular infinite
sequence
(WLOG, a sequence of all Hs) can be seen to be exactly zero by the
following
argument:
It would require an infinite tail of Hs, which is the same as having *no*
Ts
after some point, which has probability 0.
No. Probability = 0 means impossible.
No it doesn't, at least not in a mathematical context. (Maybe in a
courtroom
it does.)
Did you or did you not state the following? ;)
But notice the qualification "finite": an *infinite* sequence of Hs has
probability 0, since that would require an infinite tail of Hs, which is
the same as having *no* Ts after some point, which has probability 0.
|
I did indeed.
| Quote: | reads as: H.. is possible, since !T... is possible. big deal
|
Rubbish. "Has probability 0" is NOT mainly a synonym for "is possible". YOU
claimed that "It CAN happen, so the probability is NOT 0"; I showed that the
probability IS 0. Equivocations about the natural-language term "possible"
are just irrelevant to the fact that you got the probability thoroughly wrong.
| Quote: | You can see why I introduce basic examples to pin your meaning.
|
No, but I think I can see why you tend to change the subject a lot.
| Quote: | fun coin()
while true
if rnd>0.5 return
wend
for any number of cycles it wont necessarily halt in that time.
for infinite number of cycles there is still one possible outcome, [low,
low, low...] that
shows its impossible to prove that it halts.
It halts with probability 1 (assuming that rnd() uses some truly random
quantum process and not a deterministic pseudo-random generator). That can
be
viewed as meaning that it's allowed to fail to halt on a finite number of
runs
during an unlimited number of runs of the program. But this is entirely
aside
from the argument I've given you to address (twice, so far).
Herc : its impossible to prove that it halts
Barb : it halts with P=1
are you agreeing or disagreeing here?
|
I'm emphatically disagreeing with YOUR claim that "It CAN happen, so the
probability [of it not halting] is NOT 0".
| Quote: | some infinite sequence is possible (in the model).
As #trials approaches infinity, the probability approaches 0+.
That's actually true. And at that limit, 0+ is identically 0.
That's nonsense. At the limit there are oo combinations and P is undefined.
|
At the limit there are indeed infinite combinations, but P is a well-defined
zero (1/oo).
| Quote: | Or does 1/oo = 0 now?
It certainly does. For example, have a look at
http://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html>, item (7).
Didn't you already know that?
"these improper elements are not real numbers, and that this system of
extended real numbers is not a field."
how much mickey mouse maths do you have to use to support Cantors bogus
idiocy?
|
Apparently your super-powers do not include reading comprehension. From the
same web page:
'The above statements which define results of arithmetic operations on oo may
be considered as abbreviations of statements about determinate limit forms.
For example, -(+oo) = -oo may be considered as an abbreviation for "If x
increases without bound, then -x decreases without bound."'
So all the arithmetic relations given there, including 1/oo = 0, can be
considered to be limit statements about garden-variety REAL numbers, unlike
your supurious "+0".
| Quote: | 9 months examining all these avenues. I have to sum up, getting recognition
in Maths is not an avenue to afford shelter from the Truman Satellite.
|
No sh*t, Sherlock. Face it, if "they" are out to get you then you're going to
get got. Just lie back and think of your eventual glorious revealing of
yourself as God or Adam or whoever.
| Quote: | xxx
xxx
xxx
yyy is missing
xxx
yxx
yyx
...
look infinity of infinities because yyy is nowhere, open your eyes
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Whatever. There's really no need to add more rubbish to the pile; almost
everyone by now understands your bogus argument.
--
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| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb |
| B B a a r b b |
| BBB aa a r bbb |
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Guest
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| Posted: Tue Jul 13, 2004 5:16 am Post subject: Re: Garry Denke's Gold & Brass Plates @ Westbury White Horse |
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"Barb Knox" <see@sig.below> wrote in
| Quote: | Therein the reason we need the number 0 rule, and the number -
rule,
and the number + rule.
Only if we have all three numbers. Since 0 = + and 0 = -, there's
no real need for the other two.
Repeatedly toss a coin (infintie times)
What is the probability of HHHHHHHHHHHHHH.... ?
# desired outcomes 1
_____________________ = __________________________
# total outcomes # total outcomes
as total outcomes -> oo, P(H..) > 0
It CAN happen, so the probability is NOT 0.
No, as I pointed out to you before, if it happens a *finite* number of
times
out of an infinite set of trials then the probability is exactly 0.
Nope. It's 0, for the same reason your SetMinus({.3, .33, .333, ...},
1/3) is 0.
HAHAHA now we're splitting hairs. I'm already up to defining aleph+1
as +/oo. Its REALLY SMALL. Its so small you multiply by infinity and
only
get +.
Too bad you're not allowed to do that. A PROBABILITY is a REAL number
between
0.0 and 1.0 inclusive. Suppose the probability of every infinite
sequence
of
(mixed) Hs and Ts is some real number epsilon > 0. So if you have more
than
(1/epsilon)+1 such sequences then their total probability would be > 1,
which
is impossible. But of course there is an infinite set of such sequences,
which is thus more than (1/epsilon)+1 for any epsilon. Therefore, there
is
no
such epsilon > 0, therefore the probability = 0.
(I hope that, unlike Peter Olcott, you do not object to indirect proofs
in
general.)
As I pointed out before, the probability of any particular infinite
sequence
(WLOG, a sequence of all Hs) can be seen to be exactly zero by the
following
argument:
It would require an infinite tail of Hs, which is the same as having *no*
Ts
after some point, which has probability 0.
No. Probability = 0 means impossible.
No it doesn't, at least not in a mathematical context. (Maybe in a
courtroom
it does.)
Did you or did you not state the following? ;)
But notice the qualification "finite": an *infinite* sequence of Hs has
probability 0, since that would require an infinite tail of Hs, which is
the same as having *no* Ts after some point, which has probability 0.
I did indeed.
reads as: H.. is possible, since !T... is possible. big deal
Rubbish. "Has probability 0" is NOT mainly a synonym for "is possible". YOU
claimed that "It CAN happen, so the probability is NOT 0"; I showed that the
probability IS 0. Equivocations about the natural-language term "possible"
are just irrelevant to the fact that you got the probability thoroughly wrong.
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cite?
I said the string is infinite length, you but in claiming its finite because P=0.
Now you say P=0 doesn't mean impossible,and now is doesn't mean possible.
Just answer this question : WHY IS IT NECESSARILY FINITE?
Can you do that without using a double meaning P=0.
Remember
| Quote: | No. Probability = 0 means impossible.
No it doesn't
|
So what does this mean?
| Quote: | an *infinite* sequence of Hs has
probability 0, since that would require an infinite tail of Hs, which is
the same as having *no* Ts after some point, which has probability 0.
|
an infinite sequence of Hs has P=0 since......
let A (for absurd) = an infinite sequence of Hs has P=0
let B (for Barb) = no T's has P=0
let C (for contradictory) = P=0 does not mean impossible
How do you get B->A
YOU WROTE A since B
| Quote: |
You can see why I introduce basic examples to pin your meaning.
No, but I think I can see why you tend to change the subject a lot.
fun coin()
while true
if rnd>0.5 return
wend
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its an infinite coin toss its the same subject you moron
| Quote: |
for any number of cycles it wont necessarily halt in that time.
for infinite number of cycles there is still one possible outcome, [low,
low, low...] that
shows its impossible to prove that it halts.
It halts with probability 1 (assuming that rnd() uses some truly random
quantum process and not a deterministic pseudo-random generator). That can
be
viewed as meaning that it's allowed to fail to halt on a finite number of
runs
during an unlimited number of runs of the program. But this is entirely
aside
from the argument I've given you to address (twice, so far).
Herc : its impossible to prove that it halts
Barb : it halts with P=1
are you agreeing or disagreeing here?
I'm emphatically disagreeing with YOUR claim that "It CAN happen, so the
probability [of it not halting] is NOT 0".
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does emphatically include ignoring the question at hand?
| Quote: |
some infinite sequence is possible (in the model).
As #trials approaches infinity, the probability approaches 0+.
That's actually true. And at that limit, 0+ is identically 0.
That's nonsense. At the limit there are oo combinations and P is undefined.
At the limit there are indeed infinite combinations, but P is a well-defined
zero (1/oo).
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its irrelevant, the question is about the length of the sequene. its no use defining
P with 0 numerator as having 0 acceptable outcomes then quoting the limit value without
declaring that its a limit.
P = real / real
P = 0
-> P = 0 / real
-> number of favourable outcomes = 0
which is clearly wrong
| Quote: |
Or does 1/oo = 0 now?
It certainly does. For example, have a look at
http://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html>, item (7).
Didn't you already know that?
"these improper elements are not real numbers, and that this system of
extended real numbers is not a field."
how much mickey mouse maths do you have to use to support Cantors bogus
idiocy?
Apparently your super-powers do not include reading comprehension. From the
same web page:
'The above statements which define results of arithmetic operations on oo may
be considered as abbreviations of statements about determinate limit forms.
For example, -(+oo) = -oo may be considered as an abbreviation for "If x
increases without bound, then -x decreases without bound."'
|
Which means
1/oo = 0 is an abbreviation for lim(x->oo) 1/x = 0
That first "=" is not equals. You are better off partitioning Mickey Mouse maths
from real maths (get it?) with
1/oo <=> 0
| Quote: |
So all the arithmetic relations given there, including 1/oo = 0, can be
considered to be limit statements about garden-variety REAL numbers, unlike
your supurious "+0".
9 months examining all these avenues. I have to sum up, getting recognition
in Maths is not an avenue to afford shelter from the Truman Satellite.
No sh*t, Sherlock. Face it, if "they" are out to get you then you're going to
get got. Just lie back and think of your eventual glorious revealing of
yourself as God or Adam or whoever.
|
its a last resort to see Eve again
| Quote: |
xxx
xxx
xxx
yyy is missing
xxx
yxx
yyx
...
look infinity of infinities because yyy is nowhere, open your eyes
Whatever. There's really no need to add more rubbish to the pile; almost
everyone by now understands your bogus argument.
|
your mind is seriously messed. don't be so condescending in future your job
is not at stake because you've been lying to your pupils all this time.
what *meaningless* mathematical syntax will you pour out next? Its like finding
the computer behind the Eliza program talking to you, just syntax no understanding.
Student : this program is rigged, in your dreams its intelligent
Eliza : Tell me more about your dreams
Herc |
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1X2Willows
Guest
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| Posted: Mon Jul 19, 2004 4:14 am Post subject: Re: Any druids in Wales |
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"Kevin Jones" wrote
| Quote: | "1X2Willows" wrote in message
"Kevin Jones" wrote
They won't be moved back to Wales - [....]
Bored, Kev?
Very!
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:-D
[sorry... was out, about & offline for a week] |
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Dafydd Monks
Guest
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| Posted: Thu Jul 29, 2004 6:56 am Post subject: Re: Any druids in Wales |
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Hey, I'm welsh and I live in Wales.
TD.
"1X2Willows" <spambucket@euro-celts.dot.com> wrote in message
news:xvDKc.7648$Qu5.6200@newsread2.news.pas.earthlink.net...
| Quote: | "Kevin Jones" wrote
"1X2Willows" wrote in message
"Kevin Jones" wrote
They won't be moved back to Wales - [....]
Bored, Kev?
Very!
:-D
[sorry... was out, about & offline for a week]
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