Deeper than primes

doronshadmi · Sep 24, 2010

Robin said:
Without ~(p and ~p) being a tautology you need to demonstrate that you have a way of doing proofs.

Robin, you have missed http://www.internationalskeptics.com/forums/showpost.php?p=6365450&postcount=11706.

Robin said:
We haven't yet covered off the matter of what happens to modus ponens when you set the second term as the negation of the first.

We have covered it because ~(p and ~p) is a tautology which determines that (p and ~p) is not used in order to get some proof.

Robin said:
It is absurd to say that MP and MT are tautologies only for certain values of their terms and not for others, and then say you can use them in proofs.

It is not an absurd at all if not using (p and ~p) is a tautology.

Furthermore, please demonstrate the need of RAA in http://en.wikipedia.org/wiki/Proof_without_words or in http://books.google.com/books?id=cy...m=2&sqi=2&ved=0CBsQ6AEwAQ#v=onepage&q&f=false.

Little 10 Toes · Sep 24, 2010

doronshadmi said:
So it is about time to move on and deal with x = x, such that x does not have a strict id, which is determined by the strict n>1:1 ratio, as demonstrated in http://www.internationalskeptics.com/forums/showpost.php?p=6368575&postcount=11719.

All you have is to grasp http://www.internationalskeptics.com/forums/showpost.php?p=6367054&postcount=11713.

First of all "p" is not a qubit. Second, ratios don't go over 100%. And if you were doing a 2,1,0 ratio, you would write 1:1:1. Again, math failure. No, let's not move on. How about you answer one of my previous questions.

Little 10 Toes said:
So after several times of you having to clarify what your previous answer is, we're at the point where your definition of a domain is "A realm where the measured and the measurer are interacted". Clear as mud.

Define "interacted".

Robin · Sep 24, 2010

doronshadmi said:
Robin, you have missed http://www.internationalskeptics.com/forums/showpost.php?p=6365450&postcount=11706

You are right - let me quote it:

Direct proofs are different than indirect proofs, becuse they are not using p AND ~P at all, and this is exactly the meaning of ~(p and ~p), which means: "not using (p and ~p) in direct proofs".

Are you serious? I mean really? Are you serious???

Do you really think that?

Furthermore, please demonstrate the need of RAA in...

You might want to try actually reading your cites. Read the back cover of the book you cited where it says

"...most mathematicians would agree that they are not proofs in the formal sense...proofs without words are pictures or diagrams that help the reader see why a particular mathematical statement is true, and also to see how one could begin to go about proving it true".

Now you may have missed my request to show the proof you claim to have posted. State what it is proving and how the conclusion is demonstrated.

I have asked several times. Why are you avoiding this?

doronshadmi · Sep 24, 2010

Robin said:
You are right - let me quote it:

Are you serious? I mean really? Are you serious???

Yes. Do you have a problem to understand that the tautology ~(p AND ~p) means, using formal proof techniques, where (p AND ~p) is not used?

Robin said:
You might want to try actually reading your cites. Read the back cover of the book you cited where it says

"...most mathematicians would agree that they are not proofs in the formal sense...proofs without words are pictures or diagrams that help the reader see why a particular mathematical statement is true, and also to see how one could begin to go about proving it true".

"...most mathematicians would agree that they are not proofs in the formal sense..." or in other words, you are talking about an agreement about this subject and not about rigorous proof about this subject.

doronshadmi · Sep 24, 2010

Little 10 Toes said:
First of all "p" is not a qubit. Second, ratios don't go over 100%. And if you were doing a 2,1,0 ratio, you would write 1:1:1. Again, math failure. No, let's not move on. How about you answer one of my previous questions.

3:1 is not 1:1:1

The Man · Sep 24, 2010

doronshadmi said:
No it supports my claim as follows:

No it doesn’t .

doronshadmi said:
1) We are talking only about Cardinality.

2) σ is any infinite cardinal and μ is any cardinal.

“and given an infinite cardinal σ and a cardinal μ, there will be a cardinal κ such that μ + κ = σ if and only if μ ≤ σ. It will be unique (and equal to σ) if and only if μ < σ.”

Let’s not forget about κ Doron.

doronshadmi said:
3) The case σ – μ (where μ=0) is trivial, because 0 is not a successor of any cardinal, and we can't use the con-commutative property of subtraction, because there are no negative cardinals (in that case 0 – σ, is an invalid expression).

No Doron what makes “0 – σ” “an invalid expression” (particularly when μ < σ) is that subtraction is non-commutative.

If μ=0 (and thus μ < σ ) then κ = σ.

doronshadmi said:
4) The non-trivial case of σ – μ is considered only if μ>0, and since σ > μ, we can't use the con-commutative property of subtraction also in this case, because there are no negative cardinals (in that case μ – σ, is an invalid expression).

Doron the restriction of μ £ σ is a result of the “con-commutative property of subtraction” otherwise the result could be negative.

If μ < σ then κ = σ

Your “non-trivial case” gives the same results as your “trivial” case. So do you consider your “non-trivial case” to be “indistinguishable” from your “trivial” case, as they both give the same results? Or is it simply that you don’t apply your own criteria for determining what you consider “indistinguishable” consistently?

doronshadmi said:
5) So we are left only with σ – μ, where μ>0, and this is exactly the non-trivial case that we are dealing with.

Did you just forget about the case where μ = σ, or are you simply ignoring it?

doronshadmi said:
6) By following (1) to (5) σ – μ = σ + μ = σ , and at this non-trivial case "-" is indistinguishable from "+".

So multiplication “is indistinguishable from” division because 5*1=5/1=5?

doronshadmi said:
So by understanding (1) to (6) we immediately understand that "-" no longer gives definite results (it does not have definite results that are different form the results that are derive from "+"), exactly because it is indistinguishable from "+".

Again read the cited references

“σ - μ” gives a definite result Doron, “κ = σ ” when μ < σ. However, when μ = σ the definite results simply depend on the actual definitions of the sets involved. Again read your own cited reference, but this time try to actually understand it.

doronshadmi said:
In other words, you have only a ratio of 1:2 (50% 1 and 50% 0),

Nope, try reading the entire post instead of just one line.

doronshadmi said:
which is a local strict value between 0 and 1 local and strict values, where I also have a ratio of 2:1 (100% 1 and 100% 0), where in both cases there is non-locality among local non-strict values or local strict values.

Doron “50% 1 and 50% 0” is a TRUE:FALSE ratio of 1:1. As Little 10 Toes already noted “ratios don't go over 100%” so your “100% 1 and 100% 0” simply evaluates to a 100% contradiction .

doronshadmi said:
For example:

This form represents non-locality among local non-strict values (symmetry):

Code:

1 1 0 0 |___|

This form represents non-locality among local strict values (asymmetry):

Code:

1 0 |___| |

The current logical foundations of the mathematical science are based only on the second form,
where "superposition" is probability of (50% 1 and 50% 0), which is actually another local strict value between 0 and 1 local and strict values.

Again try actually reading the whole post this time.

doronshadmi said:
But in both forms Non-locality and Locality are involved.

Again stop simply trying to posit aspects of your own failed reasoning onto others.

doronshadmi · Sep 24, 2010

The Man said:
“50% 1 and 50% 0” is a TRUE:FALSE ratio of 1:1.

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

How "lovely".

The Man said:
It will be unique (and equal to σ) if and only if μ < σ.”

So cardinal κ is non-unique (and therefore can't be surly = σ) if μ = σ, according to this quote.

Wellcome to the kingdom of non-strict cardinals, in this case.

The Man said:
No Doron what makes “0 – σ” “an invalid expression” (particularly when μ < σ) is that subtraction is non-commutative.

No, if we deal with Cardinality and μ < σ, then the non-commutative aspect of subtraction gives an invalid expression
like “μ – σ” and a valid expression like “σ – μ”.

Another example of an invalid expression is "1/(n>1)=x" if we claim that x is a natural number.

Since invalid expressions are gibberish, then we actually use only valid expressions.

Under the consideration of using only valid mathematical expressions in the case of Cardinality, "+" and "-" are indistinguishable operations.

The Man said:
Your “non-trivial case” gives the same results as your “trivial” case.

Only if invalid mathematical expression is also a valid mathematical expression.

The Man said:
Again stop simply trying to posit aspects of your own failed reasoning onto others.

Again stop simply trying to force aspects of some limited reasoning onto others.

The Man said:
Again try actually reading the whole post this time.

Again, try actually to read and understand http://www.internationalskeptics.com/forums/showpost.php?p=6367054&postcount=11713, because reading-only is not enough.

Little 10 Toes · Sep 24, 2010

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

How "lovely".

I'm sure Juila Child used that example all the time. "Now remember, for every cup of flour used in cakes, make sure you put in 0 teaspoons of vanilla extract and 0 tablespoons of baking powder. That way you'll get the perfect ratio."

epix · Sep 25, 2010

Little 10 Toes said:
First of all "p" is not a qubit. Second, ratios don't go over 100%. And if you were doing a 2,1,0 ratio, you would write 1:1:1. Again, math failure. No, let's not move on. How about you answer one of my previous questions.

When Doron finds another proof of him not being able to handle math for 6-year-old kids, he will invent his new rules how to treat ratios and percentages "w.r.t." OM to make up for the total failure of basic reasoning that makes the cake dough.

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. Only after he finds out that his formulas no worky in the kitchens and college dorms, he starts explaining what he actually meant. When he's done, he continues to serve his strongly counter-intuitive soup.

Robin · Sep 25, 2010

doronshadmi said:
Yes. Do you have a problem to understand that the tautology ~(p AND ~p) means, using formal proof techniques, where (p AND ~p) is not used?

It doesn't even remotely mean that. Not by the wildest stretch of the imagination.

I can't imagine how someone could get it so utterly, disasterously wrong.

Anyway, let me repeat this from my last post:

Now you may have missed my request to show the proof you claim to have posted. State what it is proving and how the conclusion is demonstrated.

I have asked several times. Why are you avoiding this?

You don't actually have any proofs in your mathematics, do you?

doronshadmi · Sep 25, 2010

Definition A: That has no predecessor has "the minimal magnitude of existence".

Example: Emptiness has "the minimal magnitude of existence".

The Cardinality of Emptiness is 0.

Definition B: That has no successor has "the maximal magnitude of existence".

Example: Fullness (the opposite of Emptiness) has "the maximal magnitude of existence".

The Cardinality of Fullness is ∞.

Definition C: That has predecessor AND successor has "an intermediate magnitude of existence".

The cardinality of that has "an intermediate magnitude of existence" is x, such that 0 < x < ∞. (where < is "greater than").

- - - - - - - - - - - - - -

X is a placeholder for 0, x or ∞.

Definition D: In the case of Cardinality, "That has no predecessor, its cardinality is not a successor".

Example: X+0=X

Details:

5+0=5, where 0 is not a successor.

|infinite collection|+0=|infinite collection|, where 0 is not a successor.

∞+0= ∞, where 0 is not a successor.

Definition E: In the case of Cardinality, "That has no successor, its cardinality is not a predecessor".

Example: ∞-X= ∞

Details:

∞-5= ∞, where ∞ is not a predecessor.

∞-|infinite collection|= ∞, where ∞ is not a predecessor.

∞-∞= ∞, where ∞ is not a predecessor.

Definition F: A set exists at least as "That has no successor" AND "That has no predecessor".

Example: {} is a set , such that the outer "{""}" represents "That has no successor" AND the emptiness between the outer "{""}" represents "That has no predecessor".

Definition G: The cardinality of the members of a given set is defined by their "magnitude of existence" w.r.t Definition A or Definition B.

Examples: |{}|=0, |{{}}|=1, |{x,y,"banana"}|=3, |{1,2,3,4,5,…}|=non-strict cardinality, because no diverges collection of members has the magnitude of existence of "That has no successor", |{[0,1]}|=non-strict cardinality, because no converges collection of members has the magnitude of existence of "That has no successor".

- - - - - - - - - - - - - -

Theorem: No set is a member of itself.

Proof:

According to Definition F, a set exists even if there are no members.

According to Definition G, any Cardinality of a given set, which is defined by the magnitude of existence of some collection (or its absence),
is < ∞.

Any collection is based on members (or their absence) so no collection of members or any given member has the cardinality of ∞.

In that case the magnitude of existence of a set is not identical to any magnitude of existence of any member, and we can conclude that no set is a member of itself.

Q.E.D

In this proof we have used MP:

MP.

If P, then Q.
P.
Therefore, Q.

If

P="the cardinality of a collection (where any collection is based on members (or their absence)) < ∞",

Then.

Q=" No set is a member of itself."

P.
Therefore, Q.

doronshadmi · Sep 25, 2010

Little 10 Toes said:
That way you'll get the perfect ratio."

Which provides 0:0 (0 cakes).

doronshadmi · Sep 25, 2010

epix said:
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

epix said:
Only after he finds out that his formulas no worky in the kitchens and college dorms, he starts explaining what he actually meant.

Only after I find that I am still not understood, I use search for new ways to explain OM.

epix said:
When he's done, he continues to serve his strongly counter-intuitive soup.

Strongly counter-intuitive soup is the Cantorian claim that non-finite collections have strict Cardinality.

All we need is to get the notion of Fullness ("that has no successor").

doronshadmi · Sep 25, 2010

Robin said:
It doesn't even remotely mean that. Not by the wildest stretch of the imagination.

I can't imagine how someone could get it so utterly, disasterously wrong.

I see that you have missed the part of http://www.internationalskeptics.com/forums/showpost.php?p=6369257&postcount=11724, which shows that your argument is nothing but an agreement about the considered subject and not a rigorous proof of it.

Why are you avoiding this fact? Is it becuse you are not aware of the difference between Visual Special Learning and Auditory Sequential Learning? ( http://www.edfac.unimelb.edu.au/eldi/selage/documents/GLT-Visualspatialgift.pdf )( http://www.scribd.com/doc/21954904/Dear-Reader-Let-Us-Explore-the-Traditional-Point-of-View )( http://www.scribd.com/doc/17039028/OMDP )?

Robin said:
Anyway, let me repeat this from my last post:

Now you may have missed my request to show the proof you claim to have posted. State what it is proving and how the conclusion is demonstrated.

I have asked several times. Why are you avoiding this?

You don't actually have any proofs in your mathematics, do you?

http://www.internationalskeptics.com/forums/showpost.php?p=6372664&postcount=11731

The Man · Sep 25, 2010

doronshadmi said:
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.

However, none of these variants represent a probability distribution totaling 100% while “50% 1 and 50% 0” does. To try to put it in simpler terms for you Doron it simply means the proposition P has an equal probability of evaluation to TRUE as it does to FALSE.

doronshadmi said:
How "lovely".

How inane.

doronshadmi said:
So cardinal κ is non-unique (and therefore can't be surly = σ) if μ = σ, according to this quote.

Again read your own cited reference, it simply depends on the specific definitions of the actual sets involved and κ can “surly = σ” “if μ = σ”.

Again read your own cited reference.

( http://books.google.com/books?id=JdU...action&f=false )

Example 3 on page 87 to be exact.

doronshadmi said:
Wellcome to the kingdom of non-strict cardinals, in this case.

Sorry Doron your fiat-land “kingdom” is strictly just yours.

doronshadmi said:
No, if we deal with Cardinality and μ < σ, then the non-commutative aspect of subtraction gives an invalid expression
like “μ – σ” and a valid expression like “σ – μ”.

Wait, so your stating “No” to the assertion that the reason your expression ““0 – σ” is invalid “is that subtraction is non-commutative” then asserting “the non-commutative aspect of subtraction gives an invalid expression like “μ – σ”” when “we deal with Cardinality and μ < σ” which is your expression ““0 – σ” . Do you ever agree with yourself Doron?

doronshadmi said:
Another example of an invalid expression is "1/(n>1)=x" if we claim that x is a natural number.

Since invalid expressions are gibberish, then we actually use only valid expressions.

Again it is the non-commutative aspect of subtraction that is the reason for the μ ≤ σ restriction.

doronshadmi said:
Under the consideration of using only valid mathematical expressions in the case of Cardinality, "+" and "-" are indistinguishable operations.

So, your “non-trivial case” is “indistinguishable” from your “trivial” case, or is it simply that you don’t apply your own criteria for determining what you consider “indistinguishable” consistently?

doronshadmi said:
Only if invalid mathematical expression is also a valid mathematical expression.

Which of your expressions in your “non-trivial case” or your “trivial” case do you now consider to be an “invalid mathematical expression”?

doronshadmi said:
Again stop simply trying to force aspects of some limited reasoning onto others.

Doron if you don’t like the aspects of your own reasoning, including the “limited reasoning” you evidently simply like to ascribe to others, then find some better reasoning, but stop trying to simply pin your own limitations onto others.

doronshadmi said:
Again, try actually to read and understand http://www.internationalskeptics.com/forums/showpost.php?p=6367054&postcount=11713, because reading-only is not enough.

Again stop simply trying to posit aspects of your own failed reasoning onto others.

Robin · Sep 25, 2010

doronshadmi said:
Definition A: That has no predecessor has "the minimal magnitude of existence".

Example: Emptiness has "the minimal magnitude of existence".

The Cardinality of Emptiness is 0.

Definition B: That has no successor has "the maximal magnitude of existence".

Example: Fullness (the opposite of Emptiness) has "the maximal magnitude of existence".

The Cardinality of Fullness is ∞.

Definition C: That has predecessor AND successor has "an intermediate magnitude of existence".

The cardinality of that has "an intermediate magnitude of existence" is x, such that 0 < x < ∞. (where < is "greater than").

- - - - - - - - - - - - - -

X is a placeholder for 0, x or ∞.

Definition D: In the case of Cardinality, "That has no predecessor, its cardinality is not a successor".

Example: X+0=X

Details:

5+0=5, where 0 is not a successor.

|infinite collection|+0=|infinite collection|, where 0 is not a successor.

∞+0= ∞, where 0 is not a successor.

Definition E: In the case of Cardinality, "That has no successor, its cardinality is not a predecessor".

Example: ∞-X= ∞

Details:

∞-5= ∞, where ∞ is not a predecessor.

∞-|infinite collection|= ∞, where ∞ is not a predecessor.

∞-∞= ∞, where ∞ is not a predecessor.

Definition F: A set exists at least as "That has no successor" AND "That has no predecessor".

Example: {} is a set , such that the outer "{""}" represents "That has no successor" AND the emptiness between the outer "{""}" represents "That has no predecessor".

Definition G: The cardinality of the members of a given set is defined by their "magnitude of existence" w.r.t Definition A or Definition B.

Examples: |{}|=0, |{{}}|=1, |{x,y,"banana"}|=3, |{1,2,3,4,5,…}|=non-strict cardinality, because no diverges collection of members has the magnitude of existence of "That has no successor", |{[0,1]}|=non-strict cardinality, because no converges collection of members has the magnitude of existence of "That has no successor".

- - - - - - - - - - - - - -

Theorem: No set is a member of itself.

Proof:

According to Definition F, a set exists even if there are no members.

According to Definition G, any Cardinality of a given set, which is defined by the magnitude of existence of some collection (or its absence),
is < ∞.

Any collection is based on members (or their absence) so no collection of members or any given member has the cardinality of ∞.

In that case the magnitude of existence of a set is not identical to any magnitude of existence of any member, and we can conclude that no set is a member of itself.

Q.E.D

In this proof we have used MP:

MP.

If P, then Q.
P.
Therefore, Q.

If

P="the cardinality of a collection (where any collection is based on members (or their absence)) < ∞",

Then.

Q=" No set is a member of itself."

P.
Therefore, Q.

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.

(On a side note, you are saying that the cardinality of any set can only be one of two possible values, yes?)

doronshadmi · Sep 25, 2010

doronshadmi said:
The Man said:

No Doron what makes “0 – σ” “an invalid expression” (particularly when μ < σ) is that subtraction is non-commutative.

Click to expand...

No, if we deal with Cardinality and μ < σ, then the non-commutative aspect of subtraction gives an invalid expression
like “μ – σ” and a valid expression like “σ – μ”.

The Man said:
Wait, so your stating “No” to the assertion that the reason your expression ““0 – σ” is invalid “is that subtraction is non-commutative” then asserting “the non-commutative aspect of subtraction gives an invalid expression like “μ – σ”” when “we deal with Cardinality and μ < σ” which is your expression ““0 – σ” . Do you ever agree with yourself Doron?

Exactly, and as a result we are left only with valid expressions (μ – σ is not one of them), exactly because the considered subject is exactly Cardinality.

By using only valid expressions that are related exactly to Cardinality, the valid expressions are σ – μ = σ + μ = σ > μ > 0, and according to these valid expressions "+" and "-" are indistinguishable, which is the non-trivial case.

EDIT:

If we return to [url]http://www.internationalskeptics.com/forums/showpost.php?p=6349487&postcount=11598[/url] 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.

doronshadmi · Sep 25, 2010

Robin said:
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.

So what? ~(p and ~p) does not mean that I have to use RAA in my proof, and I definitely do not use RAA in my proof.

It does not mean that RAA can't be used in order to get some proof.

What I say is that a lot of proofs can be done without using RAA, and actually if something can be proven by ~RAA and also by RAA, then ~RAA proof is considered as more elegant than the RAA proof, in most cases.

Robin said:
(On a side note, you are saying that the cardinality of any set can only be one of two possible values, yes?)

No, I do not say that. Please look at Definition G and its examples.

The Man · Sep 25, 2010

doronshadmi said:
Exactly, and as a result we are left only with valid expressions (μ – σ is not one of them), exactly because the considered subject is exactly Cardinality.

So you were intentionally disagreeing with yourself when you said “No”, then cited the same reason I did for “μ – σ” not being valid?

doronshadmi said:
By using only valid expressions that are related exactly to Cardinality, the valid expressions are σ – μ = σ + μ = σ > μ > 0, and according to these valid expressions "+" and "-" are indistinguishable, which is the non-trivial case.

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

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

doronshadmi · Sep 25, 2010

The Man said:
So you were intentionally disagreeing with yourself when you said “No”, then cited the same reason I did for “μ – σ” not being valid?

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

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

You don't get it do you?

If we return to http://www.internationalskeptics.com/forums/showpost.php?p=6349487&postcount=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.

The Man said:
So is "μ + σ" one of your "valid expressions"?

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

The Man · Sep 25, 2010

doronshadmi said:
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 · Sep 25, 2010

The Man said:
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)

The Man said:
So is "μ + σ" one of your "valid expressions"?

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

doronshadmi · Sep 25, 2010

The Man,

The current accepted framework is 0 < μ

OM's framework is 0 < μ < ∞

The Man · Sep 25, 2010

doronshadmi said:
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.

doronshadmi said:
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 · Sep 25, 2010

doronshadmi said:
The Man,

The current accepted framework is 0 < μ

No, read the cited references.

doronshadmi said:
OM's framework is 0 < μ < ∞

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

epix · Sep 26, 2010

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.

doronshadmi said:
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 · Sep 26, 2010

doronshadmi said:
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 · Sep 26, 2010

The Man said:
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 · Sep 26, 2010

epix said:
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 · Sep 26, 2010

The Man said:
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).

The Man said:
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 ∞.

The Man said:
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.

The Man said:
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 · Sep 26, 2010

Robin said:
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 · Sep 26, 2010

The Man said:
doronshadmi said:

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

Click to expand...

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 · Sep 26, 2010

doronshadmi said:
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.

doronshadmi said:
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.

doronshadmi said:
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?

doronshadmi said:
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.

doronshadmi said:
“σ is strict” is always false.

So then your claim of

doronshadmi said:
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?

doronshadmi said:
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 · Sep 26, 2010

doronshadmi said:
The Man, we are talking about different things.

Of that, I'm sure.

doronshadmi said:
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.

doronshadmi said:
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.

doronshadmi said:
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.

doronshadmi said:
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.

doronshadmi said:
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.

Click to expand...

But we have been over all this before.

doronshadmi · Sep 26, 2010

The Man said:
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?

doronshadmi said:
The Man said:

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

Click to expand...

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 · Sep 26, 2010

The Man said:
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.

doronshadmi said:
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?

The Man said:
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.

The Man said:
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%?

The Man said:
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 Man said:
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 · Sep 26, 2010

The Man said:
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 · Sep 26, 2010

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 · Sep 26, 2010

doronshadmi said:
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.

doronshadmi said:
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?

doronshadmi said:
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 · Sep 26, 2010

doronshadmi said:
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…

The Man said:
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.

doronshadmi said:
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.

doronshadmi said:
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.

doronshadmi said:
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.

doronshadmi said:
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.

doronshadmi said:
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.

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

Nonsense

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