Deeper than primes

[The Man]

Because all of Doron’s notions and notations are, well, “non-strict”, Epix (especially when it comes to Doron’s application of them).

 

[epix]

This model can be used to understand better the differences between microscopic and macroscopic non-rotating black holes.

Are you sure?

I've seen models like that, but there was never any cosmology issue near by.

What size is that 1(0.8... anyway?

 

[The Man]

Are you sure?

I've seen models like that, but there was never any cosmology issue near by.

What size is that 1(0.8... anyway?

Perhaps he has a different "OM" meaning for "black hole" as well (at least the “non-rotating” ones anyway)?

 

[doronshadmi]

You still simply don’t understand that "≠" still isn't a location and “As a result” your “non-local property of ≠ w.r.t any given pair of 0() localities.” is still simply just nonsense.

What you say is disjoint from your understanding.

For example, you do not get that your claim that "≠" is not a location is equivalent to the claim that "≠" is non-local, and indeed ≠ is the non-locality of 1() w.r.t any distinct 0() along it, such that 1() is at AND not at w.r.t any given distinct 0().

 

[doronshadmi]

Because all of Doron’s notions and notations are, well, “non-strict”, Epix (especially when it comes to Doron’s application of them).

Because all of The Man's notions and notations are, well, “strict”-only, he can't get non-strict notions or notations.

 

[doronshadmi]

I've seen models like that, but there was never any cosmology issue near by.

epix, you can be happy by aware of the fact that I've seen models like that, and you are made of space\time stars dust.

 

[doronshadmi]

What size is that 1(0.8... anyway?

You can use ant measurement unit, but it does not change the fact that the measurement is done under Non-locality\Locality Linkage.

 

[doronshadmi]

So why did you use 1 - 0.999... instead of 1 - 0.999...9?

You can use 0.999...9 instead of 0.999... as long as "..." is understood as infinite interpolation, such that both numbers < 1 by 0.000...1

I think that the old-fashioned expression 10^-n (n → ∞) is superior in clarity to your version 0.000...1.

The old-fashioned expression is not fine enough in order to distinguish between, for example,
0.000...1[base 2] as the complement of 0.111...[base 2] to 1, or 0.000...1[base 3]as the complement of 0.222...[base 3] to 1, as seen in:

 

[doronshadmi]

Oh and evidently you simply can’t understand that a line segment is specifically not “beyond” its given end points and in the case of segment represented by an interval like (1,2) the line segment isn’t even “at” those two points.

The 1() space is exactly at AND not at any considered distinct 0().

In the case of (1,2) 0(1) OR 0(2) are simply not considered, so?

 

[epix]

Originally Posted by epix
I think that the old-fashioned expression 10^-n (n → ∞) is superior in clarity to your version 0.000...1.

The old-fashioned expression is not fine enough in order to distinguish between, for example,
0.000...1[base 2] as the complement of 0.111...[base 2] to 1, or 0.000...1[base 3]as the complement of 0.222...[base 3] to 1, as seen in:

[qimg]http://farm3.static.flickr.com/2793/4318895416_e5d2042b0c_z.jpg?zz=1[/qimg]

What do you mean? The expression is universal; it applies to all number bases. For example

1 - 2^-n where n → ∞ equals 0.1111... [base 2]

 

[The Man]

What you say is disjoint from your understanding.

No Doron, it isn't.

For example, you do not get that your claim that "≠" is not a location is equivalent to the claim that "≠" is non-local, and indeed ≠ is the non-locality of 1() w.r.t any distinct 0() along it, such that 1() is at AND not at w.r.t any given distinct 0().

So now you agree that "≠" is not a location on a line?

You still haven’t answered this question.

Are you claiming that any location “a long 1() is exactly” a point?

Again, please indentify any location on a line that is not and can not be covered by points.

Because all of The Man's notions and notations are, well, “strict”-only, he can't get non-strict notions or notations.

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

The 1() space is exactly at AND not at any considered distinct 0().

Once again, your contradictory claim, thus “exactly” and only your problem.

In the case of (1,2) 0(1) OR 0(2) are simply not considered, so?

So, it simply demonstrates once again that you have no idea what you are talking about. “In the case of (1,2)” both those point are “considered” specifically as the boundaries. What they are specifically “not considered”, however, is members of the set of points that result from that interval. Not included in the set does not mean or even infer that they “are simply not considered”, but given your “magnitude of existence” nonsense that seems a fact that you have “simply not considered”.

 

[epix]

epix, you can be happy by aware of the fact that I've seen models like that, and you are made of space\time stars dust.

Tell Henry to leave me alone. I'm taking the train to Suffragette City tomorrow.

 

[doronshadmi]

So now you agree that "≠" is not a location on a line?

Now I agree that ≠ is the non-locality of 1() w.r.t any given distinct 0() along it, such that 1() is at AND not at the given distinct 0().

Again, please indentify any location on a line that is not and can not be covered by points.

You simply can't get anything beyond distinct 0(), isn't it The Man?

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

Again, stop simply trying to posit aspects of your 0()-only reasoning onto others.

Once again, your contradictory claim, thus “exactly” and only your problem.

Once again, your contradictory claim is derived from your 0()-only reasoning, thus “exactly” and only your problem.

So, it simply demonstrates once again that you have no idea what you are talking about. “In the case of (1,2)” both those point are “considered” specifically as the boundaries.

Nonsense, (1,2) means, for example, that 1((0(1)+0.000...1())≠(0(2)-0.000...1()))

What they are specifically “not considered”, however, is members of the set of points that result from that interval. Not included in the set does not mean or even infer that they “are simply not considered”, but given your “magnitude of existence” nonsense that seems a fact that you have “simply not considered”.

No The Man, your 0()-only reasoning is too weak in order to understand expressions like (0(1)+0.000...1()) or (0(2)-0.000...1()), and how ≠ is exactly the non-locality of 1() between them.

 

[doronshadmi]

What do you mean? The expression is universal; it applies to all number bases. For example

1 - 2^-n where n → ∞ equals 0.1111... [base 2]

n^-n is a general form, but it can't be used for fine distinction, for example:

0.111...[base 2] (which is under 2^-n) ≠ 0.111...[base 3] (which is under 3^-n), as can be seen in:

It is clear that (1 - 0.1111...[base 2]) ≠ (1 - 0.1111...[base 3])

 

[doronshadmi]

Tell Henry to leave me alone. I'm taking the train to Suffragette City tomorrow.

So be aware of black holes when you are on the railroad.

 

[zooterkin]

You don't relate the operands well: the expression "0.999..." implies a number where the decimal digits repeat infinitely, whereas the result "0.000...1" implies a very small but finite number. So the subtraction 1 - 0.999... = 0.000...1 is not a good rendition of the idea of non-strictness.

We've been round this one a few times before with Doron. He thinks that
1 / 3 * 3 = 0.999...
and that this is not equivalent to 1. So, he invented the 0.000...1 notation, and thinks it means something profound.

 

[doronshadmi]

We've been round this one a few times before with Doron. He thinks that
1 / 3 * 3 = 0.999...
and that this is not equivalent to 1. So, he invented the 0.000...1 notation, and thinks it means something profound.

No zooterkin, you wrongly think that the strict number 1/3 is the non-strict number 0.333...[base 10].

You are also missing http://www.internationalskeptics.com/forums/showpost.php?p=6451665&postcount=12034.

 

[The Man]

Now I agree that ≠ is the non-locality of 1() w.r.t any given distinct 0() along it, such that 1() is at AND not at the given distinct 0().

Agree with whom, yourself? That you claim it "is at AND not at the given distinct 0()" shows that you can't even agree with yourself.

You simply can't get anything beyond distinct 0(), isn't it The Man?

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

Again, stop simply trying to posit aspects of your 0()-only reasoning onto others.

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

Once again, your contradictory claim is derived from your 0()-only reasoning, thus “exactly” and only your problem.

What contradictory claim of mine are you referring to?

Nonsense, (1,2) means, for example, that 1((0(1)+0.000...1())≠(0(2)-0.000...1()))

Nope, as explained to you many times before it means specifically that the boundary points are not included in the set of points resulting from that interval.

No The Man, your 0()-only reasoning is too weak in order to understand expressions like (0(1)+0.000...1()) or (0(2)-0.000...1()), and how ≠ is exactly the non-locality of 1() between them.

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

“≠” is still not a location on a line.

Again, please indentify any location on a line that is not and can not be covered by points.

 

[epix]

Originally Posted by epix
What do you mean? The expression is universal; it applies to all number bases. For example

1 - 2^-n where n → ∞ equals 0.1111... [base 2]

n^-n is a general form, but it can't be used for fine distinction, for example:

0.111...[base 2] (which is under 2^-n) ≠ 0.111...[base 3] (which is under 3^-n), as can be seen in:

[qimg]http://farm5.static.flickr.com/4103/5096227808_e362e07fe9_z.jpg[/qimg]

It is clear that (1 - 0.1111...[base 2]) ≠ (1 - 0.1111...[base 3])

I never mentioned n^-n. Where do you see it?

I mentioned a formula particular to base 2, where I meant by "universal" the involvement of the limit, that means n → ∞. It wasn't exactly the way I should have explained it, so that's why you tried to say that 1 - 2^-n where n → ∞ doesn't apply to other number bases apart from base 2. So I need to make amends.

The universal formula that involves the limit n → ∞ and applies to all number bases is

(aⁿ - 1)/(aⁿ⁺¹ - aⁿ) = 0.1111... [base a]

where n → ∞ and a is the number base. You can substitute finite k for n and run a few examples.

 

[epix]

No zooterkin, you wrongly think that the strict number 1/3 is the non-strict number 0.333...[base 10].

Why do you feel the need for changing the traditional description? 1/3 is the "exact form" and 0.333... is called the "approximate form." Believe it or not, the distinction have had its own description.