Deeper than primes

[jsfisher]

You willingly ignored the rest of http://www.internationalskeptics.com/forums/showpost.php?p=4763566&postcount=3258.

I wonder why?

Because it wasn't there originally. You added it while I was replying. Actually, you inserted the added content in another post first....then you moved it around and covered your trail with other re-edits.

 

[doronshadmi]

Ok jsfisher.

Please answer to (including the questions that can be found in the linked post) this:

You are using an agreed game with notations, that avoids any research of the notions that stand at the basis of the notations.

Again it is shown how your framework is limited to "how to define and\or use?" questions, and explicitly avoids "how it is?" , "what is this?" , "Why it is?" etc … questions.

In other words, you totally ignored the notions (and questions) that are expressed in http://www.internationalskeptics.com/forums/showpost.php?p=4763491&postcount=3256, in order to fit the facts to your agreed game with notations.

EDIT:

By the way, it is easy to show the inconsistency of Standard Math, in this case:

1) From one hand it claims that Y of X<Y has no immediate predecessor, and for that d must be > 0.

2) On the other hand it claims that 0.999…[base 10] = 1 , and for that d must be 0.

I know that (2) is a sum of non-finite Q members, but it has no significance in this case, because both R and Q are dense, by Standard Math.

 

[integral]

By the way, it is easy to show the inconsistency of Standard Math, in this case:

1) From one hand it claims that Y of X<Y has no immediate predecessor, and for that d must be > 0.

2) On the other hand it claims that 0.999…[base 10] = 1 , and for that d must be 0.

I know that (2) is a sum of non-finite Q members, but it has no significance in this case, because both R and Q are dense, by Standard Math.

... if I were you, I wouldn't quit my day job.

 

[doronshadmi]

... if I were you, I wouldn't quit my day job.

Please reply by following the content of the post.

 

[jsfisher]

This is an agreed game with notations, that avoids any research of the notions that stand at the basis of the notations.

No, it is not. It is a game of you seriously misunderstanding simple concepts and protecting your misunderstandings by re-interpreting the statements of others.

The following expresses the very simple notion about real numbers.

[latex]$$ \forall x \forall y, \, x < y \Rightarrow \exists z, \, x < z < y $$[/latex]​

The nice thing about first order predicates such as this, they are complete in and of themselves and don't require your re-interpretation to make sense of them.

Again it is shown how your framework is limited to "how to define and\or use?" questions, and explicitly avoids "how it is?" , "what is this?" , "Why it is?" etc … questions.

You have never shown anything like that.

In other words, you totally ignored the notions that are expressed in http://www.internationalskeptics.com/forums/showpost.php?p=4763491&postcount=3256 in order to fit the facts to your agreed game with notations.

You classic extensive post edits are extremely rude. Don't expect others to pander to your rudeness.

EDIT:

by the way, it is easy to show the inconsistency of Standard Math, in this case:

1) From one hand it claims that Y of X<Y has no immediate predecessor, and for that d must be > 0.

2) On the other hand it claims that 0.999…[base 10] = 1 , and for that d must be 0.

I know that (2) is a sum of non-finite Q members, but it has no significance in this case, because both R and Q are dense, by Standard Math.

There is no inconsistency in those two statements. In fact, they are closely related. If 0.999... were not identical to 1, then you'd have an inconsistency between statements (1) and (2).

 

[doronshadmi]

The following expresses the very simple notion about real numbers.

[latex]$$ \forall x \forall y, \, x < y \Rightarrow \exists z, \, x < z < y $$[/latex]​

The nice thing about first order predicates such as this, they are complete in and of themselves and don't require your re-interpretation to make sense of them.

Yes, jsfisher, we all know that this predicate came form the god of mathematics. No re-interpretation is needed.

EDIT:

by the way, it is easy to show the inconsistency of Standard Math, in this case:

1) From one hand it claims that Y of X<Y has no immediate predecessor, and for that d must be > 0.

2) On the other hand it claims that 0.999…[base 10] = 1 , and for that d must be 0.

I know that (2) is a sum of non-finite Q members, but it has no significance in this case, because both R and Q are dense, by Standard Math.

There is no inconsistency in those two statements. In fact, they are closely related. If 0.999... were not identical to 1, then you'd have an inconsistency between statements (1) and (2).

Do you really not get the simple and straightforward notion that 0.999...[base 10]=1 only if d=0?

If d>0 then the sum of the non-finite sequence d=0.9 + d=0.09 + d=0.009 + d=… ≠ 1

 

[jsfisher]

Do you really not get the simple and straightforward notion that 0.999...[base 10]=1 only if d=0?

If d>0 then the sum of the non-finite sequence d=0.9 + d=0.09 + d=0.009 + d=… ≠ 1

You have adopted yet another usage of your ubiquitous d. Before it was the length of an interval. Now, out of nowhere, it has become the next addend in an infinite summation.

You have failed to demonstrate any contradiction or inconsistency.

 

[doronshadmi]

You have adopted yet another usage of your ubiquitous d. Before it was the length of an interval. Now, out of nowhere, it has become the next addend in an infinite summation.

You have failed to demonstrate any contradiction or inconsistency.

Do you have abstraction problems, jsfisher?

...,it has become the next addend in an infinite summation.

There is no "next" here jsfisher.

Please try again http://www.internationalskeptics.com/forums/showpost.php?p=4763819&postcount=3266 .

 

[jsfisher]

Please try again http://www.internationalskeptics.com/forums/showpost.php?p=4763819&postcount=3266 .

There is nothing there to consider. You have taken two disjoint statements and asserted an inconsistency between them. There isn't one.

 

[The Man]

These "no gaps" of X < Z < Y hold iff (d > 0) AND (d ≠ 0).

Since Standard Math claims that the non-finite universe between X and Y is completely filled, then d must be the minimal value, which is 0.

So Standard Math in its own framework, has to decide between "completely filled" (and in this case d must be = 0) and "Y has no immediate predecessor" (and in this case d must be > 0).

As long as Standard Math insists to use both "completely filled" AND "Y has no immediate predecessor" on the same non-finite universe between X and Y, Standard Math is based on the reasoning that claims that d is both > AND = 0, which is a contradiction under Standard Math framework.

You have asked me to show a contradiction within the framework of Standard Math.

I have never asked you “to show a contradiction within the framework of Standard Math” I have simply asked you to actually learn math before you claim to be showing “a contradiction within the framework of Standard Math”

I provided such a contradiction (d is both > AND = 0).

Now, instead of face the facts, you behave like any fanatic religious community of people, which does not wish to face the facts about its own failure.

A contradiction based simply on your ignorance of the very math you claim to be contradictory. As always the failure and fanaticism remain yours.

 

[doronshadmi]

There is nothing there to consider. You have taken two disjoint statements and asserted an inconsistency between them. There isn't one.

Please prove that these "closely related" (your words) statements have nothing to do with each other.

EDIT:

If 0.999... were not identical to 1, then you'd have an inconsistency between statements (1) and (2).

So they are not disjoint, after all.

 

[jsfisher]

There is no "next" here jsfisher.

Really? Let's see...

the sum of the non-finite sequence d=0.9

Addend.

... + d=0.09

Next addend.

... + d=0.009

Next addend.

...

 

[doronshadmi]

Really? Let's see...

Addend.

Next addend.

Next addend.

Come on jsfisher think abstract, d>0 is not about any particular Q member, and you know it.

 

[jsfisher]

Come on jsfisher think abstract, d>0 is not about any particular Q member, and you know it.

Doron, you are flittering from brainstorm to brainstorm, rendering these partial thoughts as posts. You aren't writing connected ideas nor are you consistent in your presentation. If you cannot recognize that you are making shifts in your own notation, don't expect us to keep up with your plot twists.

For the 0.9999... case, what (singular) does your d represent?

 

[doronshadmi]

Doron, you are flittering from brainstorm to brainstorm, rendering these partial thoughts as posts. You aren't writing connected ideas nor are you consistent in your presentation. If you cannot recognize that you are making shifts in your own notation, don't expect us to keep up with your plot twists.

jsfisher, since your abstract ability is based on notations, you don't get tha fact that I am talking on the same notion.

For the 0.9999... case, what (singular) does your d represent?

This time please answer to http://www.internationalskeptics.com/forums/showpost.php?p=4763887&postcount=3268 .

 

[jsfisher]

jsfisher, since your abstract ability is based on notations, you don't get tha fact that I am talking on the same notion.

You misunderstand so very much.

This time please answer to http://www.internationalskeptics.com/forums/showpost.php?p=4763887&postcount=3268 .

I did, but you didn't like the response, so you ignored it. Moreover, you don't really want a response to post #3268; you really are asking for post #3266, but that, too, has already received an unliked response.

Still, much of this revolves around your meaning for d with respect to 0.9999.... Care to provide some clarity?

 

[doronshadmi]

You misunderstand so very much.



I did, but you didn't like the response, so you ignored it. Moreover, you don't really want a response to post #3268; you really are asking for post #3266, but that, too, has already received an unliked response.

Still, much of this revolves around your meaning for d with respect to 0.9999.... Care to provide some clarity?

I provided the wrong link in my last post.

Please answer to http://www.internationalskeptics.com/forums/showpost.php?p=4763918&postcount=3271 .

 

[jsfisher]

I provided the wrong link in my last post.

Please answer to http://www.internationalskeptics.com/forums/showpost.php?p=4763918&postcount=3271 .

I've added disjoint to the list of terms you don't understand.

 

[doronshadmi]

By the way, it is easy to show the inconsistency of Standard Math, in this case:

1) From one hand it claims that Y of X<Y has no immediate predecessor, and for that d must be > 0.

2) On the other hand it claims that 0.999…[base 10] = 1 , and for that d must be 0.

I know that (2) is a sum of non-finite Q members, but it has no significance in this case, because both R and Q are dense, by Standard Math.

There is no inconsistency in those two statements. In fact, they are closely related. If 0.999... were not identical to 1, then you'd have an inconsistency between statements (1) and (2).

There is nothing there to consider. You have taken two disjoint statements and asserted an inconsistency between them. There isn't one.

Here is jsfisher's self contradiction:

The phrase:

a) " If 0.999... were not identical to 1, then you'd have an inconsistency between statements (1) and (2)."

contradicts the phrase:

b) "You have taken two disjoint statements and asserted an inconsistency between them."

In phrase (a) jsfisher explicitly concludes something that is based on (1) and (2), but in phrase (b) he claims that we cannot conclude anything that is based on (1) and (2), because (1) and (2) are disjoint.

In other words, jsfisher contradicts himself.

Still, much of this revolves around your meaning for d with respect to 0.9999.... Care to provide some clarity?

Do you really not get the simple and straightforward notion that 0.999...[base 10]=1 only if d=0?

If d>0 then the sum of all elements of the non-finite sequence d=0.9 + d=0.09 + d=0.009 + d=… ≠ 1 (and there is no "next element" here because d>0 is for the all elements of this non-finite sequence).

 

[jsfisher]

Here is jsfisher's self contradiction:

The phrase:

a) " If 0.999... were not identical to 1, then you'd have an inconsistency between statements (1) and (2)."

contradicts the phrase:

b) "You have taken two disjoint statements and asserted an inconsistency between them."

In phrase (a) jsfisher explicitly concludes something that is based on (1) and (2), but in phrase (b) he claims that we cannot conclude anything that is based on (1) and (2), because (1) and (2) are disjoint.

In other words, jsfisher contradicts himself.

Learn to read, and learn what words mean. I've already told which word in particular you are misinterpreting, here.

Do you really not get the simple and straightforward notion that 0.999...[base 10]=1 only if d=0?

Do you really not get that all I asked was for you to clarify what you meant by d in this context.

If d>0 then the sum of all elements of the non-finite sequence d=0.9 + d=0.09 + d=0.009 + d=… ≠ 1 (and there is no "next element" here because d>0 is for the all elements of this non-finite sequence).

Oh, I see. You use it inconsistently. No wonder you couldn't clarify. It's not one thing; it's infinitely many things.