Deeper than primes

[doronshadmi]

“the next element” is a direct reference to ordering.

{a,b,c,d,e,...} is the ordered form of set S.

{b,c,a,e,d,...} is a non-ordered form of set S.

In both cases there is the next element, no matter if S is ordered of non-ordered.

Once again you attempt simply to take no responsibility for what you write.

Once again you attempt simply to take no responsibility for what you read, simply because you avoid using your mind in order to generalize what you read.

Instead you continue with your "cut\paste already agreed boxes" thinking style.

Nope two letters that are different ...

You don't have this difference if (as you claim) there is nothing between A and B.

Once again you demonstrate your inability to understand the fundamentals which are resulted by different A,B letters.

So your claim is now, that as usual, you’re just saying “Technically”, well, “nothing”?

So you just “Technically” can't get that "there is nothing between A and B"?

Links were given to the articles which themselves have links to other references ...

So what, still you do not use your mind in order to understand what you read exactly because you are closed under these "cut\paste already agreed boxes" thinking style, no matter if links are used by it.

Doron you still don’t grasp that just making up your own contradictory nonsense while deliberately misrepresenting and misinterpreting well established concepts and definitions certainly aren’t “new notions”.

The contradiction is a direct result of the inability of your "cut\paste already agreed boxes" thinking style to comprehend the co-existence of the smaller and the smallest.

Stop being so dang lazy Doron and actually read the linked articles and references, heck you might actually learn something like the difference between “only cut\paste”, copy/pasting relevant quotes along with the links.

I read these articles. They were written by people that (like you) can't comprehend the co-existence of the smaller and the smallest.

Again show the interval for the difference in the orderings in your pervious set example.

Again show that there is nothing between A and B and still they are different.

There is “nothing between A and B” and there are two different letters. So your assertion simply fails by its own self contradiction.

The Man, you do not comprehend the result of “nothing between A and B”.

The interval (1,1) results in the empty set so there is no “member” in that case. Your probably should have actually read the article or at the very least the quoted portions.

(1,1) or {} is resulted with no member at all, or in other words, simply nothing.

Doron you just don’t get “this fine subject” at all, you simply refuse to consider any “thinking” but your own and yours is demonstrably self-contradictory. As a result you simply don’t agree with anyone including yourself.

You agree with your own misunderstanding of this fine subject.

 

[doronshadmi]

Do you have a line segment that is “ever smaller” than your “0.00000...1”?

Yes, for example: 0.00000...1[base 10] is “ever smaller” than 0.00000...1[base 2].

 

[doronshadmi]

“no such dimensional limitation” that you simply choose to read ‘no dimensional limitation’ instead of what was written makes the nonsense, as usual simply and entirely yours.

Please define dimensional limitation < 0.

 

[epix]

Originally Posted by epix
a-a=0 is called "subtraction" and not "phase transition."

It does not change the fact that a>0 is irreducible to 0.

When you get familiar with the term "subtraction," you will find out that a - a = 0. When you test it and reach to your yummy jar containing 5 cockroaches and you eat them all, you will find out that your treats are indeed all gone and the number of cockroaches in the jar equals zero.

There is no process here, (in terms or metric space) 0-dim element can't be 0-dim element.

There is a process here except there is no name for it, coz you are the only person since 52,651 BC who claims that two identical things are necessarily different, like that 0-dim element doesn't equal 0-dim element, or 0 ≠ 0 in a general case. (No mercy, no typos. LOL.)

Your used current agreed reasoning can't comprehend the following expression:

1 - 0.999...[base 10] = 0.000...1[base 10]

Do you think that I forgot?
http://www.internationalskeptics.com/forums/showpost.php?p=7123939&postcount=15243

I could somewhat follow where that expression 0.000...1 came from. It takes a few lines of code inside an infinite loop to generate a = 0.999... Now Doron knows that a in its approximate form cannot reach 1, unless changes are made to the generating code. And so 1 - 0.999... = 0.000...1

You've invented a fictitious opponent who claims that a line segment can be repeatedly divided until there are no line sub segments left and the line segment is therefore all made of points. So once again: What is the numerator and the denominator that yield 0.000...1?

0.000...1 = d/n ?

This solution is the result of the co-existence of the smaller AND the smallest as the fundamentals of the researched form.

No. The solution is a result of co-existence of several math procedures, coz the set of two equations doesn't have an actual exact solution, only approximate one. The attempt to isolate b leads to

b = a/W(a²)

where W is called "Lambert W-Function."
http://mathworld.wolfram.com/LambertW-Function.html

That's why I chose the example of a point that can be defined in the exact form only as a solution to an equation. You can't place every point in its approximate form on a line segment -- there is no point of division 3.14159... but only point pi, for example.

Once again: There is no location on a line segment where a point couldn't be placed to indicate the location where the line segment would be divided into two line subsegment. That's why a line segment is "fully covered by points."

 

[jsfisher]

{a,b,c,d,e,...} is the ordered form of set S.

{b,c,a,e,d,...} is a non-ordered form of set S.

In both cases there is the next element, no matter if S is ordered of non-ordered.

It continues to be remarkable how much wrong can be expressed in so few lines.

 

[laca]

It continues to be remarkable how much wrong can be expressed in so few lines.

Yeah. Not to mention everyone is still waiting for the proof that any set and its power set have the same cardinality.

 

[zooterkin]

Yes, for example: 0.00000...1[base 10] is “ever smaller” than 0.00000...1[base 2].

Oh, yes, that was a good one! A fifth the size, wasn't it?

 

[doronshadmi]

It continues to be remarkable how much wrong can be expressed in so few lines.

By using your wrong reasoning, this is the best you can get, so?

 

[doronshadmi]

Oh, yes, that was a good one! A fifth the size, wasn't it?

Think about constant proportion between 0.000...1[base 10] and 0.000...1[base 2] upon infinitely many scale levels.

 

[doronshadmi]

When you get familiar with the term "subtraction," you will find out that a - a = 0. When you test it and reach to your yummy jar containing 5 cockroaches and you eat them all, you will find out that your treats are indeed all gone and the number of cockroaches in the jar equals zero.

When you get familiar with the irreducibility of 1-dim element into 0-dim element, you will be able to understand the phase trasition that stands at the basis of a - a = 0 , where a is some length > 0.

(No mercy, no typos. LOL.)

Yes I know, it fits to your state of mind that is influenced by your reasoning.

Do you think that I forgot?
http://www.internationalskeptics.com/forums/showpost.php?p=7123939&postcount=15243

You've invented a fictitious opponent who claims that a line segment can be repeatedly divided until there are no line sub segments left and the line segment is therefore all made of points.

You can't forget what you don't get, and you don't get the irreducibility of 1-dim into 0-dim.

No. The solution is a result of co-existence of several math procedures, coz the set of two equations doesn't have an actual exact solution, only approximate one. The attempt to isolate b leads to

b = a/W(a²)

where W is called "Lambert W-Function."
http://mathworld.wolfram.com/LambertW-Function.html

That's why I chose the example of a point that can be defined in the exact form only as a solution to an equation. You can't place every point in its approximate form on a line segment -- there is no point of division 3.14159... but only point pi, for example.

The non-local number 3.14159...[base 10] < the local number pi.

Once again: There is no location on a line segment where a point couldn't be placed to indicate the location where the line segment would be divided into two line subsegment. That's why a line segment is "fully covered by points."

Once again, no matter how many points there are along a given line, it is irreducible into 0-dim, where this simple fact is resulted by the inability of collection of 0-dims to completely cover a 1-dim element.

Only a sub line-segment along a given line segment has the ability to be at-once in more than one location, which is a fundamental property that no point along the given line segment has.

Once again you demonstrate your mind's limitation to get the difference between the local and the non-local.

When you test it and reach to your yummy jar containing 5 cockroaches and you eat them all, you will find out that your treats are indeed all gone and the number of cockroaches in the jar equals zero.

You still do not get the co-existence of Locality and Non-locality, which enables the existence of more than one object, in the first place.

 

[epix]

Once again, no matter how many points there are along a given line, it is irreducible into 0-dim, where this simple fact is resulted by the inability of collection of 0-dims to completely cover a 1-dim element.

LOL. No one says that the definition in question requires the line segment to be a collection of points and nothing but points, except your imaginary foe -- Count Dracula I guess, coz every count must count.
http://historeo.com/Resources/dracula.gif
1, 2, 3, and point and 4, the neck, the bite and all that gore.

 

[doronshadmi]

LOL. No one says that the definition in question requires the line segment to be a collection of points and nothing but points,

The claim that a line (or a line-segment) is totally covered by points is equivalent to the claim that a line (or a line-segment) is no more than a collection of points.

 

[The Man]

{a,b,c,d,e,...} is the ordered form of set S.

{b,c,a,e,d,...} is a non-ordered form of set S.

In both cases there is the next element, no matter if S is ordered of non-ordered.

Once again Doron both of your examples are just different orderings of the same set, evidently you just don’t understand or simply refuse to accept that fact.

Once again you attempt simply to take no responsibility for what you read, simply because you avoid using your mind in order to generalize what you read.

Once again “generalize” simply does not mean what you would apparently would like it to.

Instead you continue with your "cut\paste already agreed boxes" thinking style.

Again you continue with your non-thinking style of “just making up crap to ascribe to others”.

You don't have this difference if (as you claim) there is nothing between A and B.

No “You don't have this difference if (as you claim)” such a difference requires your “interval” and there is no such interval. The failing remains simply yours Doron no matter how much you would simply like to pawn it off onto others.

Once again you demonstrate your inability to understand the fundamentals which are resulted by different A,B letters.

Once again you fail to show any interval resulting from the differences in the letters A and B or from the different orderings of your “set S” above. The demonstrable failure remains simply yours.

So you just “Technically” can't get that "there is nothing between A and B"?

Doron you’re the one claiming there must be your “interval” between A and B for there to be your “difference”, so it is once again just you that “can’t get” it, even from just yourself.

So what, still you do not use your mind in order to understand what you read exactly because you are closed under these "cut\paste already agreed boxes" thinking style, no matter if links are used by it.

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

The contradiction is a direct result of the inability of your "cut\paste already agreed boxes" thinking style to comprehend the co-existence of the smaller and the smallest.

Nope, once again just a result of your assertions that contradict each other.

I read these articles. They were written by people that (like you) can't comprehend the co-existence of the smaller and the smallest.

Really, please show any one of those articles that claimed that “smaller and the smallest” could not ‘co-exist’?

Again show that there is nothing between A and B and still they are different.

Please show where I ever asserted there was “nothing between A and B”?

The Man, you do not comprehend the result of “nothing between A and B”.

Doron “you do not comprehend” that since it is you claiming “nothing between A and B” that it is up to you to show “there is nothing between A and B and still they are different”.

(1,1) or {} is resulted with no member at all, or in other words, simply nothing.

What, so you mean your assertion of…

You still do not get that difference is some particular case of interval, where interval is the opposite of nothing between considered things (which is always a one and only one thing, if there is nothing between the asserted things).

…is simply false?

The resulting set from the open interval (1,1) is the empty set {} while for the closed interval [1,1] it is the set {1}. Still no difference between the limits of either interval yet the results you assert as “simply nothing” for one while the other you claimed “…is always a one and only one thing, if there is nothing between the asserted things)”.

Again since your “difference” requires your “interval” please show your interval representing the difference between the open interval (1,1) and the closed interval [1,1]. That you simply want to claim that your “interval” is just something you would like to call “difference” still simply makes all the contradictions resulting from your claim just yours.

You agree with your own misunderstanding of this fine subject.

While you evidently still just don’t agree with “with your own”, apparently deliberate, “misunderstanding of this fine subject.”

Yes, for example: 0.00000...1[base 10] is “ever smaller” than 0.00000...1[base 2].

So your “ever smaller” than “0.00000...1[base 2]” isn’t “ever smaller” than your “ever smaller” than “0.00000...1[base 10]”? Looks like you still just can’t agree with yourself. What isn’t your “ever smaller” than 0.00000...1[base 10] “ever smaller” than?

Please define dimensional limitation < 0.

It’s your statement, Doron; you define it (if you can). However, if you have any specific questions, need clarification or a definition of anything I have written, I am more than happy to oblige.

 

[The Man]

The claim that a line (or a line-segment) is totally covered by points is equivalent to the claim that a line (or a line-segment) is no more than a collection of points.

Nope. Again a collection of points or even line segments can form a discrete space. While the claim “a line (or a line-segment) is totally covered by points is equivalent” to a specific reference to a continuous space. Certainly both the discrete space and the continuous space can be represented as “a collection of points”, but there is certainly more to it than just that. This is what you still seem to be deliberately ignoring Doron. Two points are “a collection of points” and at least that is required to define a line segment, to represent that line segment as a collection of points in a continuous space requires “more than a collection of” just two “points”. “a collection of points” simply lacks specificity, a lacking that you feed upon and indulge yourself in Doron, while deliberately ignoring the space that collection forms or is a subset of.

 

[jsfisher]

Yeah. Not to mention everyone is still waiting for the proof that any set and its power set have the same cardinality.

As he as done before with several other of this wrongnesses, he'll continue to ignore it for a while, then at some point circle back. He'll reassert the same wrongness he started with; he'll cycle through the same schoolyard taunts towards anyone that challenges his nonsense.

Actually, we are a bit overdue for a revisit to his menorah diagrams for numbers founded on inconsistent special cases and broken formulae. It is a masterful combination of trivia and contradiction blended into the meaningless.

 

[doronshadmi]

Once again Doron both of your examples are just different orderings of the same set, evidently you just don’t understand or simply refuse to accept that fact.

Once again The Man you demonstrate how you wrongly use order , which is equivalent to the use of straight line as some particular case of a curve (as done by agreement between professional mathematicians)

Once again “generalize” simply does not mean what you would apparently would like it to.

Since you are unable to generalize what you read, you do not have meaningful things to say about this important concept.

Again you continue with your non-thinking style of “just making up crap to ascribe to others”.

The crap is a direct result of being closed in a box too many time.

No “You don't have this difference if (as you claim)” such a difference requires your “interval” and there is no such interval. The failing remains simply yours Doron no matter how much you would simply like to pawn it off onto others.

If there is nothing between A and B, then there are no different A and B.

This is a fact that your boxes reasoning style can't comprehend.

Once again you fail to show any interval resulting from the differences in the letters A and B or from the different orderings of your “set S” above. The demonstrable failure remains simply yours.

Once again you do not understand the proposition "there is nothing between A and B.

Doron you’re the one claiming there must be your “interval” between A and B for there to be your “difference”, so it is once again just you that “can’t get” it, even from just yourself.

The Man you do not comprehend the result of "nothing between A and B"

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

Stop force your boxes reasoning on others.

Nope, once again just a result of your assertions that contradict each other.

It is exactly a reflection of your own reasoning, when you read my replies about this fine subject.

Really, please show any one of those articles that claimed that “smaller and the smallest” could not ‘co-exist’?

1) Again you need other in order to make up your mind.

2) Because of (1) you even unable to get that I claim all along this this that “smaller and the smallest” are in co-existence exactly becuse they are non-transformable into each other (their ids are not vanished under the co-existence).

Please show where I ever asserted there was “nothing between A and B”?

There is “nothing between A and B” and there are two different letters. So your assertion simply fails by its own self contradiction.

Doron “you do not comprehend” that since it is you claiming “nothing between A and B” that it is up to you to show “there is nothing between A and B and still they are different”.

No, you clearly say:

There is “nothing between A and B” and there are two different letters. So your assertion simply fails by its own self contradiction. ( http://www.internationalskeptics.com/forums/showpost.php?p=7133420&postcount=15257 )

so it is up to you.

What, so you mean your assertion of…



…is simply false?

In this case you can't comprehend the different results of "nothing between A and B" and "nothing".

The resulting set from the open interval (1,1) is the empty set {} while for the closed interval [1,1] it is the set {1}. Still no difference between the limits of either interval yet the results you assert as “simply nothing” for one while the other you claimed “…is always a one and only one thing, if there is nothing between the asserted things)”.

You look for the set, I look for the member of the set (or its absence).

Again since your “difference” requires your “interval” please show your interval representing the difference between the open interval (1,1) and the closed interval [1,1]. That you simply want to claim that your “interval” is just something you would like to call “difference” still simply makes all the contradictions resulting from your claim just yours.

Again you are unable to comprehend that difference is a particular case of interval.

While you evidently still just don’t agree with “with your own”, apparently deliberate, “misunderstanding of this fine subject.”

Again you get only your own twisted reflection, each time you are using your boxes cut\paste reasoning style in order to get what I write.

So your “ever smaller” than “0.00000...1[base 2]” isn’t “ever smaller” than your “ever smaller” than “0.00000...1[base 10]”? Looks like you still just can’t agree with yourself. What isn’t your “ever smaller” than 0.00000...1[base 10] “ever smaller” than?

Still you demonstrate your inability to get the present continuous state of some non-local number like 0.00000...1[base 10] as being ever smaller.

This is another example, out of too many examples, to comprehend this fine subject, by using your local-only reasoning.

It’s your statement, Doron; you define it (if you can). However, if you have any specific questions, need clarification or a definition of anything I have written, I am more than happy to oblige.

Nonsense.

He just can't seem to make up his mind. Whether he wants a discrete space with his self-contradictory notation of .00000...1, indicating an infinitesimal and thus a smallest line segment (basically a one dimensional yet infinitely small point). Or a continuous space with no such dimensional limitation on the minimal location.

In other words, you are the one who claim that there is no smallest under the co-existence of smaller AND smallest.

Furthermore, the equate above clearly demonstrates that you still do not grasp what I write all along this thread, about this subject.

Let us analyze your reply:

Whether he wants a discrete space with his self-contradictory notation of .00000...1, indicating an infinitesimal and thus a smallest line segment (basically a one dimensional yet infinitely small point).

The Man , smaller (where .00000...1[base 2], is some particular example of it, known as non-local number) can't be the smallest, where the smallest, in this case is exactly 0 size.

Or a continuous space with no such dimensional limitation on the minimal location.

Simply wrong, the smaller and the smallest are in co-existence in the considered complex form, which is called line segment.

 

[doronshadmi]

Nope. Again a collection of points or even line segments can form a discrete space. While the claim “a line (or a line-segment) is totally covered by points is equivalent” to a specific reference to a continuous space.

Nope. Again, the continuum is not a collection, the continuum is at least a 1-dim space, and no collection of 0-dim spaces along it reaches it (or "completely covers it" if we are using your jargon).

 

[doronshadmi]

As he as done before with several other of this wrongnesses, he'll continue to ignore it for a while, then at some point circle back. He'll reassert the same wrongness he started with; he'll cycle through the same schoolyard taunts towards anyone that challenges his nonsense.

Actually, we are a bit overdue for a revisit to his menorah diagrams for numbers founded on inconsistent special cases and broken formulae. It is a masterful combination of trivia and contradiction blended into the meaningless.

http://www.internationalskeptics.com/forums/showpost.php?p=7105665&postcount=15176

Your agreed transfinite system is a joke.

Also you can't comprehend the range between no-mapping and bijection as it found according to one's useful needs between the general form {a,b,c,d,...} and the general form {{},{a},{b},{c},{d},...,{a,b,c,d,...}}.

 

[ehcks]

.000...0001 is impossible. It is an invalid "number" that can not exist according to the use of "..." and the definition of infinity.

First, you write down an infinite number of zeroes (which is impossible in itself), then you finally decide to place a 1. But you can't, because you must instead write infinity more zeroes. Even more impossible. You can never write a 1 because no matter how many infinities-worth of zeros you've written, you must always write infinity more zeroes.

There will never be a 1. There can never be a 1.
When attempting to answer "1 - 0.999... = x", the x has the same chance of having a 1 as a binary number has of having a 2.

 

[The Man]

Once again The Man you demonstrate how you wrongly use order , which is equivalent to the use of straight line as some particular case of a curve (as done by agreement between professional mathematicians)

So your eaxmples are different orderings of the same set? By all means please show how the ordering is the same in both of your examples.

Since you are unable to generalize what you read, you do not have meaningful things to say about this important concept.

Again generalize simply doesn’t mean what you apparently would like it to.

The crap is a direct result of being closed in a box too many time.

Ah, so your crap is a direct result of some traumatic “box” experience you had? That makes more sense than anything you have claimed so far

If there is nothing between A and B, then there are no different A and B.

Again there are differences between the letters A and B, but no interval as a result. That you simply want your “interval” to be your “difference” and the opposite of “nothing between” is only your problem.

This is a fact that your boxes reasoning style can't comprehend.

Again stop simply trying to posit aspects of your own failed reasoning, and I guess traumatic “box” experiences, onto others.

Once again you do not understand the proposition "there is nothing between A and B.

Once again you do not understand that it is simply your “proposition”.

The Man you do not comprehend the result of "nothing between A and B"

So far the result has simply been your self contradictory nonsense.

Stop force your boxes reasoning on others.

Again stop simply trying to posit aspects of your own failed reasoning, and I guess traumatic “box” experiences, onto others.

It is exactly a reflection of your own reasoning, when you read my replies about this fine subject.

Nope, once again just a result of your assertions that contradict each other.

1) Again you need other in order to make up your mind.

What? That even makes less sense than you do normally, even just on its own let alone in relation to what was asked.

2) Because of (1) you even unable to get that I claim all along this this that “smaller and the smallest” are in co-existence exactly becuse they are non-transformable into each other (their ids are not vanished under the co-existence).

Since you simply decided not to even try to answer the question, I’ll have to ask it again.

Really, please show any one of those articles that claimed that “smaller and the smallest” could not ‘co-exist’?

No, you clearly say:

so it is up to you.

What is “up to” me? To point out the quotation marks around what you said?

In this case you can't comprehend the different results of "nothing between A and B" and "nothing".

Once again that seems to be just you.

You look for the set, I look for the member of the set (or its absence).

In both cases there is a set and the remarks were specifically in regard to the membership of those sets. Are your sure you even know where you are looking?

Again you are unable to comprehend that difference is a particular case of interval.

Again you are unable to show your so called “interval” for the many differences already noted.

Again you get only your own twisted reflection, each time you are using your boxes cut\paste reasoning style in order to get what I write.

Again stop simply trying to posit aspects of your own failed reasoning, and I guess traumatic “box” experiences, onto others.

Still you demonstrate your inability to get the present continuous state of some non-local number like 0.00000...1[base 10] as being ever smaller.

Still you demonstrate your inability to get even just your own notions, by not answering simple and direct questions.

This is another example, out of too many examples, to comprehend this fine subject, by using your local-only reasoning.

Again stop simply trying to posit aspects of your own failed reasoning, and I guess traumatic “box” experiences, onto others.

Nonsense.

Well if that’s how you want to define your statement, that’s up to you.

You are the one who claim that there is no smallest under the co-existence of smaller AND smallest.

Show where I have made such a claim.