Deeper than primes

[The Man]

You don't get it do you?

If we return to http://www.internationalskeptics.com/forums/showpost.php...ostcount=11598 which deals only with Cardinality, then aleph1 – aleph0 = aleph1 + aleph0 = aleph1 > aleph0 > 0, where the result aleph1 is a meaningless result because "+" and "–" are are indistinguishable.

No you still don't "get it" and evidently simply don't want to get it.

Again if you think “"+" and "-" are indistinguishable”, that is just your problem.

So is "μ + σ" one of your "valid expressions"?

 

[doronshadmi]

No you still don't "get it" and evidently simply don't want to get it.

Again if you think “"+" and "-" are indistinguishable”, that is just your problem.

Yes that this is not your problem, becuae you don't get (and evidently simply don't want to get it) the opposite of Emptiness (known as Fullness)

So is "μ + σ" one of your "valid expressions"?

If one claims that σ is strict, then this is an invalid expression.

 

[doronshadmi]

The Man,

The current accepted framework is 0 < μ

OM's framework is 0 < μ < ∞

 

[The Man]

Yes that this is not your problem, becuae you don't get (and evidently simply don't want to get it) the opposite of Emptiness (known as Fullness)

Got that a long time ago Doron. Your “direct perception” has failed you yet again.

If one claims that σ is strict, then this is an invalid expression.

So when you claim that σ is not “strict” it is one of your “valid expressions”?

When do you claim “that σ is strict” and when do you claim ‘that σ is not strict’?

How does one claiming “σ is strict” make it an “invalid expression”?

 

[The Man]

The Man,

The current accepted framework is 0 < μ

No, read the cited references.

OM's framework is 0 < μ < ∞

So, that is simply your limitation and it limits only you.

 

[epix]

Originally Posted by epix
If there is a case of a non-standard treatment, the writers always issue a big notice to alert the reader about it. Doron never does that.

What you claim is simply worng, as can be clearly seen, for example, in:

http://www.scribd.com/doc/18453171/International-Journal-of-Pure-and-Applied-Mathematics-Volume-49

http://www.scribd.com/doc/16542245/OMPT

http://www.scribd.com/doc/21967511/...considerations-of-Some-Mathematical-Paradigms

None of the text that you provided the links for shows any ratio nor mentions the word "ratio," which is the main theme of the argument. You simply decided to mutilate the way ratios are commonly applied, coz you don't understand them, as they were born out of rational thinking that you are no longer capable of. When alerted to mishandling the math basics without prior notice, you provided some links to show otherwise ("as can be clearly seen"), but nothing is clearly seen, coz the object of the argument is never mentioned in the links, which is another evidence of your complete disorientation.

Someone claims to know how to build a house. Obviously, folks wouldn't be that dumb to invest in all material and labour to see the house to decide if it was safe to occupy. Just show me your tool box and we can take it from there.

I think that OM stands for "Obvious Mistakes," not "Organic Mathematics."

 

[epix]

Yes that this is not your problem, becuae you don't get (and evidently simply don't want to get it) the opposite of Emptiness (known as Fullness)

I like that story about Christianity sweeping the corners of the world leaving all the single-task gods wondering about how to continue their existence and in what magnitude. The god of nothing turned out to be the smart one by simply converting to Christianity, even becoming a cardinal.
http://www.scribd.com/doc/16542245/OMPT

The magnitude of the existence of a set is not determined by its members if these "members" are Emptiness or Fullness. Emptiness or Fullness are not researchable directly, because Emptiness' existence on its own is too weak, and Fullness' existence on its own is too strong. For example, The Empty Set is not itself Emptiness but it is an existing thing that is used to define the Cardinal of Emptiness, where Emptiness' "existence" itself is weaker than any existing thing.

 

[doronshadmi]

No, read the cited references.




So, that is simply your limitation and it limits only you.

μ is for finite or infinte cardinality.

In other words, you are unable to get ∞, exactly because your reasoning is limited to 0 < μ.

 

[doronshadmi]

None of the text that you provided the links for shows any ratio nor mentions the word "ratio," which is the main theme of the argument. You simply decided to mutilate the way ratios are commonly applied, coz you don't understand them, as they were born out of rational thinking that you are no longer capable of. When alerted to mishandling the math basics without prior notice, you provided some links to show otherwise ("as can be clearly seen"), but nothing is clearly seen, coz the object of the argument is never mentioned in the links, which is another evidence of your complete disorientation.

Someone claims to know how to build a house. Obviously, folks wouldn't be that dumb to invest in all material and labour to see the house to decide if it was safe to occupy. Just show me your tool box and we can take it from there.

I think that OM stands for "Obvious Mistakes," not "Organic Mathematics."

epix, it is not about the concept "ratio".

It is about your claim that I do not alert the reader about non-standard treatment.

Please read again the provided links in http://www.internationalskeptics.com/forums/showpost.php?p=6372784&postcount=11733 , and you will find that your claim is wrong.

 

[doronshadmi]

Got that a long time ago Doron.

No The Man, that has Cardinality ∞ is beyond 0 < μ reasoning (where μ is the cardinality of finite of infinite non-empty collection).

So when you claim that σ is not “strict” it is one of your “valid expressions”?

Yes. And in order to get that you have to get that has Cardinality ∞.

When do you claim “that σ is strict” and when do you claim ‘that σ is not strict’?

σ (the cardinality of inifinte collection) is not strict because σ < ∞ is a tautology.

How does one claiming “σ is strict” make it an “invalid expression”?

“σ is strict” is always false.

One unables to get it if the considered framework is 0 < μ (where μ is the cardinality of finite of infinite non-empty collection).

 

[doronshadmi]

But if MP is not necessarily a tautology (as you have said it is not), obviously it cannot be used in a proof.

Using MP in a proof says that MP is necessarily a tautology, which implies that ~(p and ~p) is also a tautology.

That, in turn, implies that (p and ~ p) is a contradiction.

Robin, do you claim that ~ is essential in order to define T or F?

I ask that question, because according to your reasoning T is undefined unless ~F is defined, and F is undefined unless ~T is defined.

 

[doronshadmi]

According to your reasoning also “0% 1 and 0% 0” is a TRUE:FALSE ratio of 1:1.

Sure, as would your “100% 1 and 100% 0” or 25% 1 and 25% 0 and it is not my “reasoning” it is just the result of the values and ratio being expressed.

The Man, we are talking about different things.

By your framework 1:1 means that the magnitude of existence of left and right sides, is the same, which is right.

Let's extend this framework (expressions like 2:1, 3:1, … n:1 are not considered), in order to deal with the concept of "magnitude of existence", such that :1 (the right side of the expression) represents the maximum magnitude of existence of the considered things.

In that case:

“100% 1 and 100% 0” has a ratio of 1:1

"25% 1 and 25% 0" has a ratio of 0.25:1

“0% 1 and 0% 0” has a ratio of 0:1

where the left side represents the actual magnitude of existence and :1 (the right side of the expression) represents the maximum magnitude of existence of the considered things.

By following this notion, we can use a better notation like:

(x[a];y):1

Where:

x or y or … etc. are 0 to 1 values.

[a] or or … etc. are the considered things.

; is a separator between the considered left side expressions.

(…) is the left side of the expression.

:1 is the right side of the expression, which represents the maximum magnitude of existence of each considered thing in (…).

 

[The Man]

μ is for finite or infinte cardinality.

In other words, you are unable to get ∞, exactly because your reasoning is limited to 0 < μ.

Doron, that is a limitation only you have asserted, and once again it limits only you.

No The Man, that has Cardinality ∞ is beyond 0 < μ reasoning (where μ is the cardinality of finite of infinite non-empty collection).

No Doron μ can be any cardinality ≤ σ.

That you simply like to conflate your nonsense with “fullness” being the opposite of “emptiness” is again only your problem.

Yes. And in order to get that you have to get that has Cardinality ∞.

So μ + σ can be one of your “valid expressions” while “μ – σ” can not. Are you starting to distinguish between “"+" and "-"” yet?

σ (the cardinality of inifinte collection) is not strict because σ < ∞ is a tautology.

No Doron, simply being an assertion and limitation of yours does not make something a tautology.

“σ is strict” is always false.

So then your claim of

If one claims that σ is strict, then this is an invalid expression.

Was just superfluous nonsense as you now assert that you claim σ is never “strict”.

So μ + σ is always one of your “valid expressions” while “μ – σ” is not. Are you starting to distinguish between “"+" and "-"” yet?

One unables to get it if the considered framework is 0 < μ (where μ is the cardinality of finite of infinite non-empty collection).

Once again as that is only your asserted limitation, it remains only your problem.

 

[The Man]

The Man, we are talking about different things.

Of that, I'm sure.

By your framework 1:1 means that the magnitude of existence of left and right sides, is the same, which is right.

No Doron your “magnitude of existence” is one of those “different things” that only you are talking about and by your own assertions is apparently just cardinality.

Let's extend this framework (expressions like 2:1, 3:1, … n:1 are not considered), in order to deal with the concept of "magnitude of existence", such that :1 (the right side of the expression) represents the maximum magnitude of existence of the considered things.

Doron it's your “framework”, do with it what you will, but I still recommend that you endeavor to make it at least self-consistent as a starting point and that you stop simply trying to ascribe some aspects of it to others.

In that case:

“100% 1 and 100% 0” has a ratio of 1:1

"25% 1 and 25% 0" has a ratio of 0.25:1

“0% 1 and 0% 0” has a ratio of 0:1

Nope you still missed it, the ratio in question was TRUE:FALSE.

where the left side represents the actual magnitude of existence and :1 (the right side of the expression) represents the maximum magnitude of existence of the considered things.

So in your “framework” TRUE and FALSE must always have the same proportion? That would be rather limiting.

By following this notion, we can use a better notation like:

(x[a];y):1

Where:

x or y or … etc. are 0 to 1 values.

[a] or or … etc. are the considered things.

; is a separator between the considered left side expressions.

(…) is the left side of the expression.

:1 is the right side of the expression, which represents the maximum magnitude of existence of each considered thing in (…).

Doron we already have that (other then your superfluous “magnitude of existence” nonsense), the total probability of having an outcome is always 1, which can be the sum of any combination of probabilities including negative probabilities and probability amplitudes (which is why some particle decay modes are suppressed).


http://en.wikipedia.org/wiki/Quantum_superposition

For example, if a photon in a plus spin state has a 0.1 amplitude to be absorbed and take an atom to the second energy level, and if the photon in a minus spin state has a −0.1 amplitude to do the same thing, a photon which has an equal amplitude to be plus or minus would have zero amplitude to take the atom to the second excited state and the atom will not be excited. If the photon's spin is measured before it reaches the atom, whatever the answer, plus or minus, it will have a nonzero amplitude to excite the atom, plus or minus 0.1.

But we have been over all this before.

 

[doronshadmi]

Was just superfluous nonsense as you now assert that you claim σ is never “strict”.

So μ + σ is always one of your “valid expressions” while “μ – σ” is not. Are you starting to distinguish between “"+" and "-"” yet?

So when you claim that σ is not “strict” it is one of your “valid expressions”?

Yes. And in order to get that you have to get that has Cardinality ∞.

Are you starting to understand that my "yes" was about the valid non-strict value of σ, and no about "μ + σ" invalid expression (which is invalid because σ is considered as a strict value)?

Since σ is non-strict, then μ + σ = σ + μ > σ - μ by 2μ (where μ > 0), and only then "+" and "-" are distinct.

You simply can't get things out of your box.

 

[doronshadmi]

No Doron your “magnitude of existence” is one of those “different things” that only you are talking about and by your own assertions is apparently just cardinality.

Let's extend this framework (expressions like 2:1, 3:1, … n:1 are not considered), in order to deal with the concept of "magnitude of existence",…

The Man do you have a problem the understand something like: "Let's extend this framework …, in order to deal with the concept of "magnitude of existence"", where this extension is the measurement of the "magnitude of existence" by using values from 0 to 1?

Nope you still missed it, the ratio in question was TRUE:FALSE.

It was about the "magnitude of existence" of them, which is defined by any value from 0 to 1, and this is exactly the meaning to the extension of the concept of "magnitude of existence" beyond Cardinality.

So in your “framework” TRUE and FALSE must always have the same proportion? That would be rather limiting.

This is an example of a step-by-step reasoning. Instead of reading the whole post and then reply, you reply separately to each part of it, and as a result you don't get what you read.

The answer is No ( as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6374976&postcount=11752 ).

But since you are using, for example, "25% T and 25% F", then what is exactly the thing that has the rest 50%?

Doron we already have that (other then your superfluous “magnitude of existence” nonsense), the total probability of having an outcome is always 1, which can be the sum of any combination of probabilities including negative probabilities and probability amplitudes (which is why some particle decay modes are suppressed).

http://en.wikipedia.org/wiki/Quantum_superposition

But we have been over all this before.

Who is talking here about traditional probability? I am talking here about an extension of the measurement of the "magnitude of existence" by using values from 0 to 1.

the total probability of having an outcome is always 1

So , according to the traditional probability, please tell us what is the outcome if the inputs are "0% True AND 0% False" ?

 

[doronshadmi]

the total probability of having an outcome is always 1

So what is the outcome of "-25% T and 25% F"?

Is it 100% of "50% F AND 50% T"?

 

[Little 10 Toes]

doron, here's a question that can help you. What is the outcome of a roulette ball landing in a plaid slot on a standard roulette wheel?

 

[The Man]

Are you starting to understand that my "yes" was about the valid non-strict value of σ, and no about "μ + σ" invalid expression (which is invalid because σ is considered as a strict value)?

What? So you were answering some question in your head instead of what was asked?

Doron, most of us here have gotten your propensity for that quite early on.

Since σ is non-strict, then μ + σ = σ + μ > σ - μ by 2μ (where μ > 0), and only then "+" and "-" are distinct.

Oh, so now “"+" and "-" are distinct.” in spite of what you have been claiming for pages.

Do you ever agree with yourself Doron?

You simply can't get things out of your box.

“You simply can't get things”, evidently even just in your own fiat-land.

 

[The Man]

The Man do you have a problem the understand something like: "Let's extend this framework …, in order to deal with the concept of "magnitude of existence"", where this extension is the measurement of the "magnitude of existence" by using values from 0 to 1?

Doron do you have a problem with understand something like…

Doron it's your “framework”, do with it what you will, but I still recommend that you endeavor to make it at least self-consistent as a starting point and that you stop simply trying to ascribe some aspects of it to others.

Because evidently you still do have such problems.

It was about the "magnitude of existence" of them, which is defined by any value from 0 to 1, and this is exactly the meaning to the extension of the concept of "magnitude of existence" beyond Cardinality.

Doron you have yet to give your concept of "magnitude of existence" any specific “meaning” other then very loosely associating it to cardinality.

This is an example of a step-by-step reasoning. Instead of reading the whole post and then reply, you reply separately to each part of it, and as a result you don't get what you read.

This is another example of you simply trying to posit some aspect of your own failed “reasoning” onto others.

The answer is No ( as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6374976&postcount=11752 ).

Doron each one of your examples in that post has the same 1:1 TRUE:FALSE ratio.

But since you are using, for example, "25% T and 25% F", then what is exactly the thing that has the rest 50%?

Where was I using an example of "25% T and 25% F" and what was it specifically identified to be an example of?

Read the whole post Doron.

Who is talking here about traditional probability? I am talking here about an extension of the measurement of the "magnitude of existence" by using values from 0 to 1.

Oh, so you’re just talking about your “extended” nonsense again. Who could have guessed? Doron you still haven’t established what your "magnitude of existence" is (other than very loosely associating it to cardinality) nor have you established how this “measurement” of yours is accomplished. So you go run off and extend anything you think you need to, but until you definitively establish it first you’re just extending your nonsense, again.

So , according to the traditional probability, please tell us what is the outcome if the inputs are "0% True AND 0% False" ?

Nonsense