Deeper than primes

[zooterkin]

I'm waiting for the penny to drop for Anders Lindman...

 

[doronshadmi]

I haven't seen such a claim. But I haven't read much of this thread. I started posting when the thread was already very long.

It is very simply, the expression "2" is not the same as the expression "{2}".

In general jsfisher belongs to a tradition, which claims that a line is completely covered by points.

I show that the reasoning of this tradition is based on contradiction because some distinct 0-dimensional space can't be = AND ≠ to another distinct 0-dimensional space along a 1-dimensional space, or in other words ≠ is actually the permanent existence of an uncovered 1-dimensional space, which is the non-locality that exists between any arbitrary given pair of localities like 0-dimensional spaces (points) upon infinitely many levels, where this uncovered 1-dimensional space is simultaneously at and beyond the location of any given 0-dimensional space (point) along it.

No 0-dimensional space (point) has this property, and as a result any given 0-dimensional space has simultaneously one and only one location w.r.t to any given space, whether this given space is 0-dim or 1-dim.

I actually show that Non-locality and Locality are the qualitative building-blocs that enables the existence of Quantity, and not vice versa.

 

[sympathic]

It is very simply, the expression "2" is not the same as the expression "{2}".

Wow! and we all needed to wait for OM to tell us that!

 

[doronshadmi]

Wow! and we all needed to wait for OM to tell us that!

Most people simply get it, but no professional mathematicians like jsfisher, for example.

 

[sympathic]

Most people simply get it, but no professional mathematicians like jsfisher, for example.

"2" is the number 2. "{2}" is the set containing the number 2 as its only member. I think every "professional mathematician" will agree the two are not the same.

 

[laca]

I'm waiting for the penny to drop for Anders Lindman...

You must have missed his threads...

 

[zooterkin]

You must have missed his threads...

Ah, a different penny drops. I'll just sit back, then.

 

[epix]

In general jsfisher belongs to a tradition, which claims that a line is completely covered by points.

I show that the reasoning of this tradition is based on contradiction because some distinct 0-dimensional space can't be = AND ≠ to another distinct 0-dimensional space along a 1-dimensional space, /snip/

The fact that any point on a defined line can be located is not supported by your "can't be = AND ≠ to another 0-dimensional space" nonsense. It only takes to ask you for the nth time which number is missing from set R to prove that you are not in control of the mechanism that supplies you with the scattered visions that you suffer from.

 

[doronshadmi]

The fact that any point on a defined line can be located is not supported by your "can't be = AND ≠ to another 0-dimensional space" nonsense. It only takes to ask you for the nth time which number is missing from set R to prove that you are not in control of the mechanism that supplies you with the scattered visions that you suffer from.

The fact that you do not understand the total locality of a given 0-dimensional space (point) along a 1-dimensional space (line), does not prevent the inability of a point to be simultaneously at one and only one location w.r.t the line, and does not prevent from the line to be simultaneously at more than one location w.r.t the point, such that there is always an uncovered line w.r.t to any amount of points along it.

Because of this fact 0.999…[base 10] < 1 by 0.000…1[base 10], where the expression "…1" of 0.000…1[base 10] is the uncovered 1-dimesional space w.r.t any cardinality of some collection of 0-dimensional spaces along it.

You are a weird case epix, because you agree with me that 0.999…[base 10] < 1, but you doing your best in order to show that I am wrong about this subject.

 

[epix]

The fact that you do not understand the total locality of a given 0-dimensional space (point) along a 1-dimensional space (line), does not prevent the inability of a point to be simultaneously at one and only one location w.r.t the line, and does not prevent from the line to be simultaneously at more than one location w.r.t the point, such that there is always an uncovered line w.r.t to any amount of points along it.

Because of this fact 0.999…[base 10] < 1 by 0.000…1[base 10], where the expression "…1" of 0.000…1[base 10] is the uncovered 1-dimesional space w.r.t any cardinality of some collection of 0-dimensional spaces along it.

You are a weird case epix, because you agree with me that 0.999…[base 10] < 1, but you doing your best in order to show that I am wrong about this subject.

Aproximate forms, such as 0.999..., are never used in transformations and/or proofs. The aproximate form is a conversion from the exact to the radix format in order to apply the result of some math operation. Or have you ever seen expression, like log 356 Fahrenheit? The concept of the limit doesn't prevent locating a point between the limit and f(x). Once again, if your novel aproximate expression 0.000...1 is the difference between 1 and 0.999..., then it is not a point, but a segment line, which can be further divided. I'm tired of repeating the same thing . . .

1 - 0.9 = 0.1 -------> 0.1/2 = 0.05 --------> new point p = 0.9 + 0.05

1 - 0.99 = 0.01 -------> 0.01/2 = 0.005 --------> new point p = 0.99 + 0.005

1 - 0.999 = 0.001 -------> 0.001/2 = 0.0005 --------> new point p = 0.999 + 0.0005

And so on toward "1 - 0.999... = 0.000...1".

Stop thinking in terms of approximate formats, otherwise you will keep believing that your invention "0.000...1" is the smallest and indivisible difference or whatever it represents in your head.

 

[doronshadmi]

Stop thinking in terms of approximate formats, otherwise you will keep believing that your invention "0.000...1" is the smallest and indivisible difference or whatever it represents in your head.

You contradict yourself.

Since 0.000...1[base 10] is a non-strict value, it can't be the smallest existing value under [base 10], because being smallest is being strict value (for example 0 or 1), and 0.000...1[base 10] is a non-strict and therefore it is simultaneously smaller than any strict or non-strict value > 0 that exists under [base 10] AND it is also > 0.

You simply do not understand that the magnitude of existence of 1-dimensional space is stronger than the magnitude of existence of any given infinite collection of 0-dimensional spaces along it, such that the magnitude of any collection of 0-dimensional spaces is inaccessible w.r.t the magnitude of 1-dimensional space, where 0.000...1[base 10] is some example of this inaccessibility.

 

[laca]

Since 0.000...1[base 10] is a non-strict value, it can't be the smallest existing value under [base 10], because being smallest is being strict value (for example 0 or 1), and 0.000...1[base 10] is a non-strict and therefore it is simultaneously smaller than any strict or non-strict value > 0 that exists under [base 10] AND it is also > 0.

You simply do not understand that the magnitude of existence of 1-dimensional space is stronger than the magnitude of existence of any given infinite collection of 0-dimensional spaces along it, such that the magnitude of any collection of 0-dimensional spaces is inaccessible w.r.t the magnitude of 1-dimensional space, where 0.000...1[base 10] is some example of this inaccessibility.

Fixed that for you. You cannot have a digit after infinity of zeros. Try to understand that. It's easy, really.

 

[zooterkin]

Fixed that for you. You cannot have a digit after infinity of zeros. Try to understand that. It's easy, really.

Yes, but this goes up to eleven infinity plus one...

 

[sympathic]

Fixed that for you. You cannot have a digit after infinity of zeros. Try to understand that. It's easy, really.

It is easy for someone who understands what infinity means. Doron does not and does not wish to understand either.

 

[doronshadmi]

Fixed that for you. You cannot have a digit after infinity of zeros. Try to understand that. It's easy, really.

0.000...1 is an expression of the inability of a collection of 0-dimensional spaces to be 1-dimensional space, and the inability of 1-dimensional space to be 0-dimensional space.

Try to understand that. It's easy, really.

 

[doronshadmi]

It is easy for someone who understands what infinity means. Doron does not and does not wish to understand either.

It is easy for someone who understands what infinity means. sympathic does not and does not wish to understand either, because he refuses to understand the difference between actual infinity like the non-locality of 1-dimensional space, and potential infinity, like a collection 0-dimensional spaces that can't be a 1-dimensional space, no matter what is the cardinality of this collection.

 

[laca]

0.000...1 is an expression of the inability of a collection of 0-dimensional spaces to be 1-dimensional space, and the inability of 1-dimensional space to be 0-dimensional space.

No. It's the expression of your inability to grasp basic mathematical concepts. By the way, any luck publishing anything? Some results from using OM? Maybe you should start working on those, eh?

 

[sympathic]

It is easy for someone who understands what infinity means. sympathic does not and does not wish to understand either, because he refuses to understand the difference between actual infinity like the non-locality of 1-dimensional space, and potential infinity, like a collection 0-dimensional spaces that can't be a 1-dimensional space, no matter what is the cardinality of this collection.

I see he is back to being a parrot. Well, parrots probably don't understand infinities as well. No surprise there.

 

[doronshadmi]

I see ...

No, you don't.

 

[epix]

You contradict yourself.

Since 0.000...1[base 10] is a non-strict value, it can't be the smallest existing value under [base 10], because being smallest is being strict value (for example 0 or 1), and 0.000...1[base 10] is a non-strict and therefore it is simultaneously smaller than any strict or non-strict value > 0 that exists under [base 10] AND it is also > 0.

I think that you are experiencing total collapse of reason and that also obscured the meaning of the word "contradiction." Let me remind you:

Because of this fact 0.999…[base 10] < 1 by 0.000…1[base 10], where the expression "…1" of 0.000…1[base 10] is the uncovered 1-dimesional space w.r.t any cardinality of some collection of 0-dimensional spaces along it.

You continue to violate the rule that prohibits aproximate numerical formats to enter math arguments. Now you came up with another "novelty" and that's the expression "...1" which is a length of a line segment that, according to you, can be no longer divided, coz the points of divisions cannot be located on that line segment that represents the expression. Even though you have been shown that any real number is divisible, you hold "...1" indivisible. You don't bother to classify your novelty expressions and if you do, you omit to supply definitions, and if you don't forget, then the definiens include other "novelty terms."

If I ask you whether "...1" is a real number or not, you will reply that is is a non-local, non-strict... The truth of the matter is that "...1" is non-local, non-strict non-sense.

Since "...1" is real non-sense, then it must be a real number and therefore it is divisible, and if it is divisible, then the points of division do exist, and since the field of real numbers is infinitely divisible by definition, then there are infinitely many locations on that line segment that represents "...1" where you can point your finger on. End of proof.