Deeper than primes - Continuation

Kage · Apr 20, 2013

doronshadmi said:
Infinity is the power of a given dimensional space > 0 w.r.t lower dimensional spaces on it, such that no amount of these dimensional spaces has the power of that dimensional space.

One of the main results of this notion, is the irreducibility of such dimensional space into a lower dimensional space (and again, do not get "dimensional space" only in terms of metric space).

How does a space have power on subspaces?

How many different infinities are there? It seems that you are suggesting that there is a hierarchy of infinities based on each space. Unfortunately, Cantor did a lot of work on this already and the cardinality of R is the same as the cardinality of Rⁿ.

Your argument is circular in that you have defined infinity based on your notion of what constitutes a space and now use that definition in order to justify your notions.

doronshadmi · Apr 20, 2013

Kage said:
How does a space have power on subspaces?

No amount of subspaces have the power of that space, exactly because it is not composed by subspaces.

Kage said:
How many different infinities are there? It seems that you are suggesting that there is a hierarchy of infinities based on each space. Unfortunately, Cantor did a lot of work on this already and the cardinality of R is the same as the cardinality of Rⁿ.

Once again you still try to understand infinity only in terms of collection.

Kage said:
Your argument is circular in that you have defined infinity based on your notion of what constitutes a space and now use that definition in order to justify your notions.

On the contrary, your notion of infinity is circular under the notion of collections.

My notion of infinity is not circular exactly because it goes beyond the concept of collections.

In other words, your notion of infinity (which is based on collections) is a potential infinity w.r.t the power of a given non-composed dimensional space > 0.

Furthermore, no amount of non-composed dimensional spaces has the power of YESthing (that has no successor).

For more details please this time read http://www.scribd.com/doc/97823738/Unity-Awarness and http://www.scribd.com/doc/98276640/Umes .

epix · Apr 21, 2013

doronshadmi said:
Let's look at this phrase:

"But the magnitude of t is increasing with each step performed in the generating formula F. For each step in F, there is one indexed epsilon."

It is wrong since an expression like "0.999...₁₀ is taken at once as exactly one infinite non-local number, where no steps (and I would say collections of finite non-local values, which are known as finite local values by Traditional Mathematics) of the forms 0.9₁₀, 0.99₁₀, 0.999₁₀, ..., etc. along it are involved, in order to define it (in terms of sets, the member of {0.999...₁₀} is not a member of {0.9₁₀, 0.99₁₀, 0.999₁₀, ...}).

Of course it is not when clearly

0.999...₁₀ = {0.9₁₀, 0.99₁₀, 0.999₁₀, ...}

Kage · Apr 21, 2013

doronshadmi said:
No amount of subspaces have the power of that space, exactly because it is not composed by subspaces.

You didn't answer the question. The word "power" here is not defined and is not a commonly accepted mathematical term.

doronshadmi said:
Once again you still try to understand infinity only in terms of collection.

I have defined infinity as a symbol representing growing without bound. It has nothing to do with "collection."

doronshadmi said:
On the contrary, your notion of infinity is circular under the notion of collections.

My notion of infinity is not circular exactly because it goes beyond the concept of collections.

Your argument is circular because it references itself. You state that spaces cannot be "composed" of lower dimensional subspaces. You then state that the power of infinity is determined by the space, which means that spaces cannot be "composed" of lower dimensional subspaces.

Your definition of infinity is non-existent. You talk about what it does, not what it is.

doronshadmi said:
In other words, your notion of infinity (which is based on collections) is a potential infinity w.r.t the power of a given non-composed dimensional space > 0.

Furthermore, no amount of non-composed dimensional spaces has the power of YESthing (that has no successor).

For more details please this time read http://www.scribd.com/doc/97823738/Unity-Awarness and http://www.scribd.com/doc/98276640/Umes .

You aren't proving anything. You just state things like "non-composed dimensional space" without any framework. You have to make these terms exact and understandable by the rest of us before we are going to care about them.

Kage · Apr 22, 2013

doronshadmi said:
Furthermore, no amount of non-composed dimensional spaces has the power of YESthing (that has no successor).

For more details please this time read http://www.scribd.com/doc/97823738/Unity-Awarness and http://www.scribd.com/doc/98276640/Umes .

See, here is the problem: Your papers are very, very hard to read. You don't seem to understand that "definition," "axiom," "lemma," and "proof." all mean specific things. You say "definition" a lot, but then say things like "non-composed" or can't be made from. These aren't definitions. These are lemmas and need some supporting work.

For someone seeking to "unify philosophy and mathematics" you don't have a clear understanding of mathematics. Mathematical proofs can be highly visual. Cantor proved the un-countability of the reals using a diagram. The fact that R² has the same cardinality as R is proven graphically. Yes you need to explain things reasonably to be taken seriously. Yes that involves words.

You need to make your work accessible to people who are not inside of your head. That means you have to explain things using reason and logic. Guess what? Mathematics is a pure language of reason. If you do not want to play by those rules you should talk your work elsewhere.

Here is the bottom line -- your work has led you to think that you can say that .999... is not equal to 1. Prove that it behaves differently (using MATH) in a way that we can understand. Don't use fake numbers like .0...01 or the like. Prove it using sound arguments and pictures if you would like.

doronshadmi · Apr 22, 2013

Kage said:
The word "power" here is not defined and is not a commonly accepted mathematical term.

I disagree with you because:

1) The word "power" is a commonly accepted mathematical term (please look at the links that are related to mathematics in https://www.google.co.il/#q="the+po...09,d.d2k&fp=5e2f9d156cef3961&biw=1272&bih=631 )

2) I use the term "power of the continuum" as a property which is related to a given non-composed dimensional space > 0, w.r.t any possible amount of lower non-composed dimensional spaces or sub-spaces (which are mixed (and therefore) composed results of several non-composed dimensional spaces) on it.

Kage said:
I have defined infinity as a symbol representing growing without bound. It has nothing to do with "collection."

"Growing without bound" is exactly the inability of infinitely many lower non-composed dimensional spaces and/or sub-spaces (as described above) to reach the non-locality of a given higher dimensional space (which is not necessarily a metric space). In other words, infinitely many objects can't be but unbounded collections.

Kage said:
Your argument is circular because it references itself. You state that spaces cannot be "composed" of lower dimensional subspaces. You then state that the power of infinity is determined by the space, which means that spaces cannot be "composed" of lower dimensional subspaces.

Each one of k-dimensional spaces (such that k = 0 to infinite amounts) is non-composed, but the relations among k-dimensional spaces under an arbitrary higher k-dimensional space > 0, provide collections of non-composed elements and\or composed objects, where no amount of lower non-composed dimensional spaces and\or composed objects of such collections, has the power of infinity of the given higher k-dimensional space > 0.

Kage said:
Your definition of infinity is non-existent.

I is your true as long as you get it only in terms of collections with unbounded amount of members (without the understanding of why they growing without bound (exactly because they can't reach the power of infinity (the non-composed state) of a given higher (non-composed) k-dimensional space (which is not necessarily a metric space).

Kage said:
You talk about what it does, not what it is.

Wrong, I clearly talk about the non-locality of a given higher (non-composed) k-dimensional space (which is not necessarily a metric space), that can't be reached by any given amount of lower non-composed dimensional spaces and\or composed objects, on it.

Kage said:
You aren't proving anything.

No the contrary, I provide the reasoning to understand why infinity in terms of collections is essentially unbounded or, in your own words, "growing without bound" (as I show above).

Kage said:
You just state things like "non-composed dimensional space" without any framework. You have to make these terms exact and understandable by the rest of us before we are going to care about them.

Wrong, I clearly provide verbal_symbolic AND visual_spatial framework, which enables to deal with things like "non-composed dimensional space ≥ 0".

It is clearly not the traditional reasoning, which is derived only from verbal_symbolic brain skills of the discussed subject (this traditional reasoning is clearly seen by your own following words: "I have defined infinity as a symbol representing growing without bound" (in other words, no visual_spatial brain skills are also used by you in order to define infinity).

Kage said:
You have to make these terms exact and understandable by the rest of us before we are going to care about them.

You have to used also your visual_spatial brain skills of the discussed subject, if you which to understand terms that are defined exactly by using verbal_symbolic AND visual_spatial brain skills. (since when your under totally depends.

Kage said:
... understandable by the rest of us before we are going to care about them.

In other words, you ask for a reasoning that is derived from using verbal_symbolic AND visual_spatial brain skills, to be expressed only by verbal_symbolic brain skills (of the discussed subjects).

Please free your mind by let it go beyond verbal_symbolic brain skills (of the discussed subjects).

If you do that we are in the first stage in order to develop some communication between us.

laca · Apr 22, 2013

Do tell, doron, why would anyone want to develop communication with you? All the evidence you provided in all these decades proves beyond any doubt that you have absolutely nothing of interest to say.

doronshadmi · Apr 22, 2013

Kage said:
Cantor proved the un-countability of the reals using a diagram. The fact that R² has the same cardinality as R is proven graphically.

Cantor is quoted as saying:

"The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type." ( http://en.wikipedia.org/wiki/Absolute_Infinite )

Another part from the link above:

"The Absolute Infinite is mathematician Georg Cantor's concept of an "infinity" that transcended the transfinite numbers. Cantor equated the Absolute Infinite with God.[1] He held that the Absolute Infinite had various mathematical properties, including the reflection principle which says that every property of the Absolute Infinite is also held by some smaller object."

What I call absolute infinity is exactly the non-locality of a non-composed dimensional space > 0, that can't be reached by any amount of lower non-composed dimensional spaces or sub-spaces (which are mixed (and therefore) composed results of several non-composed dimensional spaces) on it).

In other words, Cantor's mathematical conception of infinity is closed under the concept of collection (which is weaker than absolute infinity (and unlike Cantor, I exclude God (or any other supreme being that governs the world) from the discussed subject).

doronshadmi · Apr 22, 2013

Let's look at the following part, taken from ( http://en.wikipedia.org/wiki/Absolute_Infinite ):

"...He held that the Absolute Infinite had various mathematical properties, including the reflection principle which says that every property of the Absolute Infinite is also held by some smaller object."

The non-local property of some higher non-composed dimensional space > 0 can be reflected in some smaller non-composed dimensional space > 0, if the smaller non-composed dimensional space > 0 is not entirely at the domain of the higher non-composed dimensional space > 0 (for example, an unbounded line, which is perpendicular w.r.t an unbounded plane, is non-local w.r.t that plane since it is at AND not at the domain of that plane (of course that plane is non-local w.r.t that line since it is at AND not at the domain of that line)).

But no collection of non-composed lower dimensional spaces is non-local w.r.t to a given higher dimensional space > 0, if the elements of that collection are entirely at the domain of the given higher dimensional space > 0.

In that case, no amount of elements of that collection reaches the non-locality of the given higher dimensional space > 0.

Let S be a collection of |R| unbounded lines that are perpendicular w.r.t a given unbounded plane.

In that case, each unbounded line is non-local w.r.t the given unbounded plane, but no amount of the intersection points of the perpendicular lines with that plane, reaches the non-locality of that plane.

doronshadmi · Apr 23, 2013

Some corrections of what I wrote in http://www.internationalskeptics.com/forums/showpost.php?p=9170434&postcount=2246 .

Instead of

"You have to used also your visual_spatial brain skills of the discussed subject, if you which to understand terms that are defined exactly by using verbal_symbolic AND visual_spatial brain skills. ~~(since when your under totally depends.~~

It has to be

"You have to use also your visual_spatial brain skills of the discussed subject, if you which to understand terms that are defined exactly by using verbal_symbolic AND visual_spatial brain skills."

doronshadmi · Apr 23, 2013

At this stage I can conclude that the traditional mathematician can't contribute any useful detailed argument about http://www.internationalskeptics.com/forums/showpost.php?p=9167235&postcount=2220 .

His/her "best" is phrases like "Instead, you wave your hands and stomp your feet like a child. Histrionics are no substitute for mathematics." of the discussed subject.

doronshadmi · Apr 23, 2013

Kage said:
Is "non-local" a fancy way of saying "made up?

No, it is defined as the irreducibility of some arbitrary higher dimensional space > 0 into any amount of lower non-composed dimensional spaces or sub-spaces (which are mixed (and therefore) composed results of several non-composed dimensional spaces) on it.

Kage said:
I get that you are trying to make some sort of "glue" to hold the number line together, but it is quite firmly constructed out of the rationals via cuts.

The cuts (including the rationals) are constructed as collection exactly because they are on the same higher non-composed dimensional space > 0, where no amount of the members of that collection reaches the non-local property of that non-composed dimensional space > 0.

doronshadmi · Apr 23, 2013

doronshadmi said:
In addition to what I wrote to you about the inability to conclude anything about "0.999..." expression, by using finite indexes, let's look at the following:

Kage said:

It is not a finite index. Hard to imagine there being that many numbers, but there are.

Click to expand...

There are infinitely many finite deltas (for example: 1 - 0.9, 1 - 0.99, 1 - 0.999, etc. at infinitum) which no one of them < 1 - 0.999... , exactly because each delta is determined by using a number with finite amount of 9s.

So, your argument that there is a "delta such that 1/epsilon is less than 1/delta" is a false argument.

Kage · Apr 23, 2013

doronshadmi said:
There are infinitely many finite deltas (for example: 1 - 0.9, 1 - 0.99, 1 - 0.999, etc. at infinitum) which no one of them < 1 - 0.999... , exactly because each delta is determined by using a number with finite amount of 9s.

So, your argument that there is a "delta such that 1/epsilon is less than 1/delta" is a false argument.

You misunderstand the argument. The argument proves that whichever delta you pick, there is a smaller epsilon. You cannot maintain that .999... and 1.0 are delta apart, no matter how small the delta, ergo they are the same number.

Show us some mathematical way that .999... and 1.0 behave differently.

Kage · Apr 24, 2013

doronshadmi said:
No, it is defined as the irreducibility of some arbitrary higher dimensional space > 0 into any amount of lower non-composed dimensional spaces or sub-spaces (which are mixed (and therefore) composed results of several non-composed dimensional spaces) on it.

You cling to this one, but it is not true. R and R² have the same cardinality.

doronshadmi said:
The cuts (including the rationals) are constructed as collection exactly because they are on the same higher non-composed dimensional space > 0, where no amount of the members of that collection reaches the non-local property of that non-composed dimensional space > 0.

Half open sets on M, the set of rational numbers are isomorphic to R. They can be defined to have all the same properties of the real numbers. I really dont care if it is composed or whatever term you like if they act the same. You insist that the real number line R cannot be constructed from the rationals, but it can.

doronshadmi · Apr 24, 2013

Kage said:
You misunderstand the argument. The argument proves that whichever delta you pick, there is a smaller epsilon. You cannot maintain that .999... and 1.0 are delta apart, no matter how small the delta, ergo they are the same number.

Show us some mathematical way that .999... and 1.0 behave differently.

According to your proof delta < and > epsilon, as follows:

Kage said:
2)
Assume that .999.... does not equal 1
Therefore, there exists a difference, epsilon = 1 - .9999...
For each epsilon, choose a delta such that 1/epsilon is less than 1/delta and that delta is a power of 10 (with Log(delta) = k).
This exists as there is no upper bound to the rational numbers.
delta is less than epsilon.
However, delta is 10^(-k) = 1 - .99..9 (with k 9s).
This implies delta is greater than 1 - .99999999.... (because there are more 9s) which is a contradiction.
Therefore .9999999... is equal to 1, QED.

But your proof does not provide even a one case, which supports your argument that you can "choose a delta such that 1/epsilon is less than 1/delta".

All you did is to show that for any arbitrary delta (out of infinitely many deltas) there is a smaller epsilon, so you can't concluded anything about 0.999... and 1 by using a delta that can't be smaller than epsilon.

doronshadmi · Apr 24, 2013

Kage said:
You cling to this one, but it is not true. R and R² have the same cardinality.

So what, the power of |R| (which is related to collections of objects on a given non-composed 1-dimesional space) is less that the power of the non-composed 1-dimesional space, exactly because a non-composed 1-dimesional space is irreducible into the composed state of a given collection on it.

Kage said:
Half open sets on M, the set of rational numbers are isomorphic to R. They can be defined to have all the same properties of the real numbers. I really dont care if it is composed or whatever term you like if they act the same. You insist that the real number line R cannot be constructed from the rationals, but it can.

No, I claim that no infinitely many objects (no matter what conclusions are found among them) that can't be but a collection (which is a composed mathematical entity) can be a non-composed dimensional space > 0 (and in this particular case the power of |R| < the power of a non-composed 1-dimensional space).

Kage said:
I really dont care if it is composed or whatever ...

In that case you support my claim that you actually do not use also your visual_spatial brain skills, in order to get notions that are not closed under the concept of collection (that can't be but a composed mathematical entity).

I also see that you ignored http://www.internationalskeptics.com/forums/showpost.php?p=9170466&postcount=2248, http://www.internationalskeptics.com/forums/showpost.php?p=9170658&postcount=2249 and http://www.internationalskeptics.com/forums/showthread.php?p=9175325#post9175325 .

doronshadmi · Apr 24, 2013

Kage said:
Show us some mathematical way that .999... and 1.0 behave differently.

If "mathematical way" is not limited only to verbal_symbolic reasoning, then http://www.internationalskeptics.com/forums/showpost.php?p=9161741&postcount=2203 is a rigorous proof that 1. and 0.999...₁₀ are not the same.

laca · Apr 24, 2013

doronshadmi said:
If "mathematical way" is not limited only to verbal_symbolic reasoning,

Translation: if we don't let reality and logic get in the way...

then http://www.internationalskeptics.com/forums/showpost.php?p=9161741&postcount=2203 is a rigorous proof that 1. and 0.999...₁₀ are not the same.

You make me laugh. You wouldn't know rigorous or proof if they came up to you together and kicked you in the balls.

Kage · Apr 24, 2013

doronshadmi said:
According to your proof delta < and > epsilon, as follows:

But your proof does not provide even a one case, which supports your argument that you can "choose a delta such that 1/epsilon is less than 1/delta".

All you did is to show that for any arbitrary delta (out of infinitely many deltas) there is a smaller epsilon, so you can't concluded anything about 0.999... and 1 by using a delta that can't be smaller than epsilon.

Yes. The proof started with "Assume .999... is different than 1" and resulted in a contradiction without further assumptions. This means that the assumption is incorrect.

No individual case is necessary. The proof holds for all deltas.

Kage · Apr 24, 2013

doronshadmi said:
If "mathematical way" is not limited only to verbal_symbolic reasoning, then http://www.internationalskeptics.com/forums/showpost.php?p=9161741&postcount=2203 is a rigorous proof that 1. and 0.999...₁₀ are not the same.

I've already told you that this picture shows that 1/2 is not 1. The red line in the base 3 case is equal to 1/3 + 1/9 + 1/27... = 1/2. .222... in base 3 is the same as .111... in base 2, as I have proven before.

Comparing the two graphs only shows the relative rate of convergence. They both converge to the same number. There is nothing there that is rigorous or a proof.

Kage · Apr 24, 2013

doronshadmi said:
Cantor is quoted as saying:

"The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type." ( http://en.wikipedia.org/wiki/Absolute_Infinite )

Another part from the link above:

"The Absolute Infinite is mathematician Georg Cantor's concept of an "infinity" that transcended the transfinite numbers. Cantor equated the Absolute Infinite with God.[1] He held that the Absolute Infinite had various mathematical properties, including the reflection principle which says that every property of the Absolute Infinite is also held by some smaller object."

What I call absolute infinity is exactly the non-locality of a non-composed dimensional space > 0, that can't be reached by any amount of lower non-composed dimensional spaces or sub-spaces (which are mixed (and therefore) composed results of several non-composed dimensional spaces) on it).

In other words, Cantor's mathematical conception of infinity is closed under the concept of collection (which is weaker than absolute infinity (and unlike Cantor, I exclude God (or any other supreme being that governs the world) from the discussed subject).

An interesting read. It does not change that R is constructed from the rationals, and that the cardinality of (a,b) in R is the same as R and that R² has the same cardinality as R.

This also doesn't change that 1/10^infinity is 0.

Kage · Apr 24, 2013

doronshadmi said:
Let's look at the following part, taken from ( http://en.wikipedia.org/wiki/Absolute_Infinite ):

"...He held that the Absolute Infinite had various mathematical properties, including the reflection principle which says that every property of the Absolute Infinite is also held by some smaller object."

The non-local property of some higher non-composed dimensional space > 0 can be reflected in some smaller non-composed dimensional space > 0, if the smaller non-composed dimensional space > 0 is not entirely at the domain of the higher non-composed dimensional space > 0 (for example, an unbounded line, which is perpendicular w.r.t an unbounded plane, is non-local w.r.t that plane since it is at AND not at the domain of that plane (of course that plane is non-local w.r.t that line since it is at AND not at the domain of that line)).

But no collection of non-composed lower dimensional spaces is non-local w.r.t to a given higher dimensional space > 0, if the elements of that collection are entirely at the domain of the given higher dimensional space > 0.

In that case, no amount of elements of that collection reaches the non-locality of the given higher dimensional space > 0.

For someone who claims to like visual-spacial reasoning, you use a lot of made up words. This makes it very difficult to follow what you are saying.

You keep claiming that higher dimensional spaces are not made up of lower dimensional spaces. They are.

doronshadmi said:
Let S be a collection of |R| unbounded lines that are perpendicular w.r.t a given unbounded plane.

In that case, each unbounded line is non-local w.r.t the given unbounded plane, but no amount of the intersection points of the perpendicular lines with that plane, reaches the non-locality of that plane.

R are is not a number. You can't have a collection of R. You are trying to use your pre-conceived notions of what a space and line are, and then apply that the mathematics.

Rⁿ is defined as (x₁, x₂,...,x_n) s.t. x_i are elements of R. R is not made up of parallel lines as you describe. it is also exactly constructed out of R.

Kage · Apr 24, 2013

doronshadmi said:
So what, the power of |R| (which is related to collections of objects on a given non-composed 1-dimesional space) is less that the power of the non-composed 1-dimesional space, exactly because a non-composed 1-dimesional space is irreducible into the composed state of a given collection on it.

I keep telling you that your use of the term "power" is circular. You say that the power of a space comes from its not being "composed" of lower dimensional spaces, and then say that a key insight of this is that spaces cannot be composed from lower dimensional spaces.

doronshadmi said:
No, I claim that no infinitely many objects (no matter what conclusions are found among them) that can't be but a collection (which is a composed mathematical entity) can be a non-composed dimensional space > 0 (and in this particular case the power of |R| < the power of a non-composed 1-dimensional space).

I have yet to see this supported by any reasoned argument. I can claim whatever I want. What makes people care is when that claim is supported.

doronshadmi said:
In that case you support my claim that you actually do not use also your visual_spatial brain skills, in order to get notions that are not closed under the concept of collection (that can't be but a composed mathematical entity).

I'll get whatever notions you articulate, provide they are not made of up unintelligible gibberish.

doronshadmi said:
I also see that you ignored http://www.internationalskeptics.com/forums/showpost.php?p=9170466&postcount=2248, http://www.internationalskeptics.com/forums/showpost.php?p=9170658&postcount=2249 and http://www.internationalskeptics.com/forums/showthread.php?p=9175325#post9175325 .

You repeat yourself a lot. Asking people to respond in writing to your every post is a bit much.

doronshadmi · Apr 25, 2013

Kage said:
I can claim whatever I want. What makes people care is when that claim is supported.

Again, your claim that there is "a delta such that 1/epsilon is less than 1/delta" is a false claim, since "for all deltas" this is not the case that delta < epsilon, if one uses your construction method of deltas.

Furthermore, your claim that there is more than 1 epsilon is a false claim, so "For each epsilon, choose a delta" (as quoted from what you call a proff) has no basis.

Kage said:
R are is not a number. You can't have a collection of R.

I wrote |R| (and not just R), as you wrongly claim), where |R| is a transfinite number, and I can have a collection |R| members.

doronshadmi · Apr 25, 2013

Kage said:
I keep telling you that your use of the term "power" is circular. You say that the power of a space comes from its not being "composed" of lower dimensional spaces, and then say that a key insight of this is that spaces cannot be composed from lower dimensional spaces.

Let me to correct you.

I say that the power of a given non-composed dimensional > 0 is > the power of any amount of lower non-composed dimensional spaces or sub-spaces (which are mixed (and therefore) composed results of several non-composed dimensional spaces) on it.

No circularity is involved here.

doronshadmi · Apr 25, 2013

Kage said:
For someone who claims to like visual-spacial reasoning, you use a lot of made up words. This makes it very difficult to follow what you are saying.

It is verbal_symbolic AND visual_spatial reasoning. Any attempt to get it by using only visual_spatial reasoning or only verbal_symbolic reasoning is designed to fail.

Kage said:
You keep claiming that higher dimensional spaces are not made up of lower dimensional spaces. They are.

No, they are not made up of lower dimensional spaces, if every dimensional pace > 0 is axiomatically taken as a non-composed mathematical entity.

This is done only if at least verbal_symbolic AND visual_spatial brain skills are used.

doronshadmi · Apr 25, 2013

Kage said:
I've already told you that this picture shows that 1/2 is not 1.

The result of the long addition 1/3 + 1/9 + 1/27 + ... can't reach 1/2 exactly because no amount of localities along the non-composed 1-dimensional space (that is located simultaneously at 0 and 1/2), has the power of that non-composed 1-dimasioal space.

Any attempt to get it by using only visual_spatial reasoning or only verbal_symbolic reasoning is designed to fail.

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

NOthing is that has no predecessor (it is below the abstract or non-abstract realm of members).

YESthing is that has no successor (it is above the abstract or non-abstract realm of members).

Kage, since Traditional Mathematics does not explicitly define NOthing and YESthing it can't deal with the inaccessibility of members into NOthing or YESthing.

YESthing is exactly the non-composed property of any dimensional space > 0 (http://www.internationalskeptics.com/forums/showpost.php?p=9170658&postcount=2249) which is inaccessible by any amount of members on it.

I think that you have no problem to understand that NOthing in itself is weaker than any amount of members.

Why do you have a problem to understand that YESthing in itself is stronger than any amount of members?

Please look at this:

"Transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite." ( http://en.wikipedia.org/wiki/Transfinite_number )

My mathematical framework (unlike the traditional Cantorean framework, which gets the absolutely infinite only in terms of collections) deals with the absolutely infinite, such that no transfinite cardinality (which is a measurement unit of a given infinite collection) is accessible into the *absolutely infinite (YESthing).

*(http://www.internationalskeptics.com/forums/showpost.php?p=9170466&postcount=2248 , http://www.internationalskeptics.com/forums/showpost.php?p=9170658&postcount=2249)

doronshadmi · Apr 27, 2013

Kage said:
This also doesn't change that 1/10^infinity is 0.

^infinity (also notated as ^∞) is a concept (and not a number) according to Traditional Mathematics, so it can't be used by it in order to get a result like 0 = 1/10^∞.

jsfisher · Apr 27, 2013

doronshadmi said:
^infinity (also notated as ^∞) is a concept (and not a number) according to Traditional Mathematics, so it can't be used by it in order to get a result like 0 = 1/10^∞.

Numbers are concepts, too, you know.

If your sole point in missing the point of the original post is to observe that infinity is not a real number, fine. You have belabored the obvious. On the other hand, there is nothing wrong with considering the reals extended to include ∞. Fundamental arithmetic operations are well-behaved with an appropriate change to the rule set.

You, yourself, Doron, have relied on this in the past. Why the sudden hypocrisy now?

doronshadmi · Apr 27, 2013

By Extended real number line ( http://en.wikipedia.org/wiki/Extended_real_number_line ) 1/∞ = 0, where ∞ is not a real number.

It does not change the fact that this result can't be defined by the traditional real number line, as expressed in http://www.internationalskeptics.com/forums/showpost.php?p=9176509&postcount=2262 (which according to it ∞ is just a concept and not a number (exactly as, for example, the concept "justice" is not a number ( http://mathforum.org/library/drmath/view/62486.html )).

One may say (by using Traditional Mathematics) that the limit of the expression "1/∞" is 0, yet, it is not the same as 1/∞ = 0.

In other words, this phrase

"Numbers are concepts, too, you know.

If your sole point in missing the point of the original post is to observe that infinity is not a real number, fine. You have belabored the obvious. On the other hand, there is nothing wrong with considering the reals extended to include ∞. Fundamental arithmetic operations are well-behaved with an appropriate change to the rule set.

You, yourself, Doron, have relied on this in the past. Why the sudden hypocrisy now?"

adds nothing to the discussed subject.

jsfisher · Apr 28, 2013

doronshadmi said:
One may say (by using Traditional Mathematics) that the limit of the expression "1/∞" is 0, yet, it is not the same as 1/∞ = 0.

Well, that sounds more like something you'd find in Doronetics. It's nonsense. Perhaps you were thinking of something less nonsensical? Like perhaps the limit of 1/N as N approaches infinity is 0? But since Doronetics has never worried about getting anything right, I sort of doubt it.

In other words, this phrase

"Numbers are concepts, too, you know...."

adds nothing to the discussed subject.

Only for one and only one person in this thread.

Still, though, Doron, instead of trying to insult a subject rather than understand it, how about you focus on your own Doronetics and its results. Surely after all these years of deep contemplation, you must have something to show. Anything?

doronshadmi · Apr 28, 2013

I assume that Dr. Wallace's (Drexel university) answer in http://mathforum.org/library/drmath/view/62486.html marks him\her as a person who does not understand Math, by the traditional mathematician here.

Actually, by the traditional mathematician here "the limit of 1/N as N approaches infinity is 0" is the same as "X is actually 0 as N goes to infinity."

Here is another example from Traditional Mathematics about this subject

" Consider the following sequence: 1.79, 1.799, 1.7999,... It can be observed that the numbers are "approaching" 1.8, the limit of the sequence.

Formally, suppose a1, a2, ... is a sequence of real numbers. It can be stated that the real number L is the limit of this sequence, namely:

$9f720022194fbcc2a121af7cc24a3ff2.png$

" ( http://en.wikipedia.org/wiki/Limit_(mathematics) ).

In other words, by this expression we actually reach L = 1.8

In other words, by Traditional Mathematics "approaching" and "reaching" have no difference, in case of the discussed subject.

It certainly impossible for a person that agrees that "approaching" is the same as "reaching", to understand a result like 0.000...1₁₀ = 1 - 0.999...₁₀, where the "...1" part of that number (0.000...1₁₀) is the irreducibility of ___ (non-composed) 1-dimensional space into 0-dimensional space (known as a point).

AdMan · Apr 28, 2013

LOL

Nobody believes this crap. Just curious, why do you insist on pushing it here?

doronshadmi · Apr 28, 2013

AdMan said:
LOL

Nobody believes this crap. Just curious, why do you insist on pushing it here?

It has nothing to do with belief.

For more details, please look at http://www.scribd.com/doc/97823738/Unity-Awarness and http://www.scribd.com/doc/98276640/Umes.

I see that you are marked as a philosopher under your nick name, so please use your philosophical abilities in order to reply in details to the provided links.

Thanks.

jsfisher · Apr 28, 2013

doronshadmi said:
I assume that Dr. Wallace's (Drexel university) answer in http://mathforum.org/library/drmath/view/62486.html marks him\her as a person who does not understand Math, by the traditional mathematician here.

What would make you say that? Reading comprehension issues again?

Actually, by the traditional mathematician here "the limit of 1/N as N approaches infinity is 0" is the same as "X is actually 0 as N goes to infinity."

No.

Here is another example from Traditional Mathematics about this subject

" Consider the following sequence: 1.79, 1.799, 1.7999,... It can be observed that the numbers are "approaching" 1.8, the limit of the sequence.

Formally, suppose a1, a2, ... is a sequence of real numbers. It can be stated that the real number L is the limit of this sequence, namely:

[qimg]http://upload.wikimedia.org/math/9/f/7/9f720022194fbcc2a121af7cc24a3ff2.png[/qimg] " ( http://en.wikipedia.org/wiki/Limit_(mathematics) ).

In other words, by this expression we actually reach L = 1.8

In other words, by Traditional Mathematics "approaching" and "reaching" have no difference, in case of the discussed subject.

Too bad you didn't bother including the rest of the last sentence in you copy/paste from Wikipedia. It wouldn't have mattered, though, I suppose.

Doron, dear Doron, did you not notice the quotation marks used with the word, approaching? Do you have even the vaguest idea why they were used? Did you also notice that the word, reaching, does not appear in the Wiki article? Do you have the vaguest idea why that is?

doronshadmi · Apr 28, 2013

The phrase "What would make you say that? Reading comprehension issues again?" is another example of the twisted maneuvers of the traditional mathematician here about the content of http://mathforum.org/library/drmath/view/62486.html.

In this case the traditional mathematician here ( by using the phrase "Numbers are concepts, too, you know.") ignores the examples (given by this link) of infinity as a concept that can't be used as a number in the case of an expression like "1/infinity".

I also claim that by Traditional Mathematics "approaching value of a given limit" and "the value of a given limit" are different.

The traditional mathematician here can't understand that the approaching value 0.999...₁₀ is not the limit value 1.

It is certainly impossible for a person that agrees that the approaching value 0.999...₁₀ is the same as the limit value 1, to understand a result like 0.000...1₁₀ = 1 - 0.999...₁₀, where the "...1" part of that number (0.000...1₁₀) is the irreducibility of ___ (non-composed) 1-dimensional space into 0-dimensional space (known as a point).

The phrase "For the case at hand, show that 1 and 0.999... behave differently in some circumstance." demonstrates the inability to distinguish, for example, between the approaching value 0.999...₁₀ and the limit value 1, which is derived, for example, from the inability to understand the the irreducibility of ___ (non-composed) 1-dimensional space into 0-dimensional space (known as a point).

The the inability to understand the the irreducibility of ___ (non-composed) 1-dimensional space into 0-dimensional space (known as a point) is typical to persons that do not used verbal_symbolic AND visual_spatial skills, in order to deal with this fine subject.

jsfisher · Apr 28, 2013

doronshadmi said:
The phrase "What would make you say that? Reading comprehension issues again?" is another example of the twisted maneuvers of the traditional mathematician here about the content of http://mathforum.org/library/drmath/view/62486.html.

Curious you say that, then in your very next sentence provide yet another example of your limitations processing basic English and employing simple logic.

In this case the traditional mathematician here ( by using the phrase "Numbers are concepts, too, you know.") ignores the examples (given by this link) of infinity as a concept that can't be used as a number in the case of an expression like "1/infinity".

You are the one raising the whole "is a concept" construct. You are the one who tried to separate "infinity" from "numbers" by observing that the former was a concept. Well, the later is a concept, too, so your attempt to distinguish the two failed miserably. (That is not to say they are not different, just that you failed to establish any difference. So what else is new.)

And then you cap it off by exposing your source for the statements you plagiarized and that you didn't understand its context nor the audience for which it was intended.

If you are going to steal someone else's work, Doron, at least try to understand it first.

I also claim that by Traditional Mathematics "approaching value of a given limit" and "the value of a given limit" are different.

"Value of a given limit"? More comprehension issues, I see. Is that like the value of 4? Just the limit, not value of the limit.

"Approaching ~~value of~~ a given limit"? That's not particularly meaningful without more context. Did you have in mind some sequence, perhaps, say {0.9, 0.99, 0.999, ...}?

You could certainly talk about that sequence "approaching" some value, but that would be a colloquial expression lacking precision. Let's identify the members of the sequence as S_i, where S₁ is 0.9, and S₂ is 0.99, and so on. Then we could note that for all j>0 that S_j+1 is closer to 1 then S_j. If that's getting at what you meant by "approaching", well, then ok, but verb forms used to describe the state of something static (like a sequence in this case) can mislead those weak on conceptual foundation. Under appropriate caveats, the sequence approaches 1 and the limit of the sequence is 1.

Other than to demonstrate your own confusion, Doron, why would you continue to embroil everything in so much incomplete and imprecise descriptions of things? Can't you tidy up your thinking just a tiny bit? Actually get to the end of one thought before trying to express the next?

The traditional mathematician here can't understand that the approaching value 0.999...₁₀ is not the limit value 1.

The "approaching value"? Have you invented yet another useless term? ...then erected a strawman around it? Seriously, what are you trying to say?

Are you completely unaware that 0.999... is a notational convenience for an infinite summation? Are you completely unaware that infinite summations rely on limits? If you have something to say about 0.999..., work from the sum; you've let the notation mislead you.

jsfisher · Apr 28, 2013

ETABWOP:^*

doronshadmi said:
I also claim that by Traditional Mathematics "approaching value of a given limit" and "the value of a given limit" are different.

Oh, dear! You did mean "approaching value" instead of "approaching [the] value", didn't you? Noun form, not verb. So you are making up more new and useless terms to obscure your own confusion.

So, pray tell, what is the definition of "approach value"?

^*Edit To Add By Way Of a Post

doronshadmi · Apr 28, 2013

A typical phrase of a person that can't understand the irreducibility of a non-composed 1-dimesional space into 0-dimesional space, is expressed as follows:

"Are you completely unaware that 0.999... is a notational convenience for an infinite summation? Are you completely unaware that infinite summations rely on limits? If you have something to say about 0.999..., work from the sum; you've let the notation mislead you."

Again, this is how verbal_symbolic-only reasoning works.

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