Deeper than primes

[epix]

epix, you can't grasp that strict 0(x) value can't be = AND ≠ to strict 0 value.

In other words, no given level of existence is completely covered by any collection of previous levels of existence.

Well, I really can't grasp it, but you should stick with the ethics and not mention certain taboos. There are social taboos, but there are also academic taboos. The traditional math is inconsistent and one of the cases that demonstrates it is the one that you keep complaining about and the essence of that case is that the traditional math asserts A = B and at the same time A ≠ B. More specifically, it is the case of identity and difference that you complain about and should not. Any ethical mathematician looks the other way, but you are an OM mathematician not fond of the traditional math, so that explains the breach of the taboo.

You didn't mention a particular case of the contradiction that may be responsible for so many problems unsolved -- problems that the best mathematicians have been trying to crack, but to no avail. Perhaps if I describe a particular case of the inconsistency based on that horrendous contradiction, you may find some solution to the predicament -- if I'm that naive.

Suppose that a person wants to travel from point A to point B.

A_________________B

But that individual cannot control all the circumstances connected with the intended activity. Obviously, the following case (1) cannot equal at the same time case (2).

1) A____________B
2) A______ ____B

But the traditional math asserts that it can.

Definition: A line is not continuous if at least one point on it is not defined by the function that creates such a line.

Here is an example of such a discontinuity; it is function

f(x) = (x² - 4)/(x - 2)

This function is not defined for x = 2, coz the function returns result 0/0 and that's why the blue straight line is not continuous at point x = 2.

The applied consequence is that you cannot finish your intended trip -- the bridge is gone. But the traditional math asserts that you can.

You see that there is a function

g(x) = x + 2

that entirely covers the blue line drawn by f(x) and therefore

f(x) = g(x)

But the identity suffers from a contradiction; namely, the point x = 2 that is not defined for f(x) is defined for g(x):

f(x=2) = (2² - 4)/(2 - 2) = 0/0 [division by zero]
g(x=2) = 2 + 2 = 4

Here is the contradiction in more formal view:

If f(x) = g(x) then f(x=2) = g(x=2) and therefore 'not defined' = '4'

Facing such a catastrophe, it is commanding to make sure that f(x) really equals g(x) using algebra. Since

x² - 4 = (x - 2) ∙ (x + 2)

it follows that

f(x) = (x² - 4)/(x - 2) = [(x - 2) ∙ (x + 2)]/(x - 2) = [(x - 2) ∙ (x + 2)]/(x - 2) = x + 2 = g(x)

and the contradiction holds.

This contradiction is a result of a much broader logical inconsistency that regards quantum/analog reasoning, and it appears in the results many a scientific field come up with. For example in

1) Simian DNA______ _______Human DNA
2) Simian DNA______________Human DNA

The evolution of human species is a theory that is allowed to exist despite the presence of various "missing links," coz

If f(x) = g(x) then (1) = (2).


You've been feverishly working for two years to collapse the world of ours, Doron, but Jesus is our Savior, and He will make sure that we will continue to live in mental darkness, happily ever after the way Adam and Eve were supposed to and free of uncertainties the source of which we cannot fix. Surely, some bridges will collapse, some planes will crash due to the f(x) = g(x) design, but we can make other attributes and continue to believe in academic Santa Klaus.

 

[doronshadmi]

Can you provide an example of some function that you notate "f()" -- function with a certain level of strictness, as it exists non-strictly?

Where does the level of strictness appear in the term X()? Is it inside the parenthesis, or is it outside? Does f(2) mean that the function f() has the second level of strictness? You never mentioned that there are certain levels of strictness.

Just provide an example of two functions of the second and the third level of strict existence, so the difference could be seen. Follow the example of the traditional function: For x = 5

f(x) = 2x + 3 = 2*5 + 3 = 13

Again, X (in terms of existence) thet is expressed as X(), can be strict ( for example PI() ), or non-strict ( for example 3.14…[base 10]() ).

The relations between non-strict 3.14…[base 10]() and strict PI() can be non-complex ( for example: ∞( PI() , 3.14…[base 10]() ) ) or complex ( for example: ∞( PI(3.14…[base 10]()) ) ).

In the case of complexity OM uses X(x) form, where X or x can be strict, or non-strict.

For example: according to OM, 3.14...[base 10](PI()) is X(x) false expression, where PI(3.14...[base 10]()) is true X(x) expression.

Does f(2) mean that the function f() has the second level of strictness?

No. f(2) is based on X(x) that is the general form of Complexity, where X(x) (such that X can be strict or non-strict) has sub-level x (such that x can be strict or non-strict).

By following the notion of non-complexity, X() exists independently of x, such that ∞( X() , x ), where your given particular case is ∞( f() , 2 ).

Does f(2) mean that the function f() has the second level of strictness?

No, it simply means that:

1) We are using X(x), which is the general form of complexity.

2) Your chosen particular expression under (1) is the strict function f(x) = 2x + 3 = 13

 

[doronshadmi]

Do you think you can actually learn what the symbols “≤” and “≥” represent, evidently you simply do not want to.

As you're the only one making that ridiculous and nonsensical claim Doron, only you can stop making it and stop trying to attribute it to others. Or can you?

Your 0()-only reasoning simply can't get that the claim that "1-dim space is completely covered by 0-dim spaces" is equivalent to the claim that (for example) "variable x ( where x is any arbitrary distinct member of [0,1] ) is both ≤ 1 OR both ≥ 0".

Both claims are definitely a contradiction.

 

[doronshadmi]

However, in a continuous space there is always at least another point between any two points.

It can't help you to avoid ≠ between some arbitrary distinct pair.

For example: the ...1 of 0.000...1[base 1] is equivalent to ≠ between 0.999...[base 10] and 1, if we avoid mixed bases.

 

[doronshadmi]

Definition: A line is not continuous if at least one point on it is not defined by the function that creates such a line.

Wrong. 1-dim space exists independently of any sub-levels of existence along it, where 0-dim space is such sub-level of existence.

OM expresses this notion as 1(0()).

 

[doronshadmi]

No one has ever argued anything like that. You are still confused by the meaning of the term explained here:
http://www.internationalskeptics.com/forums/showpost.php?p=6485624&postcount=12134

Once again . . .
Let x be a positive integer. Then

65 ≤ x ≤ 75 means that x can take on values from 65 to 75.

65 < x < 75 means that x can take on values from 66 to 74.

65 < x ≤ 75 means that x can take on values from 66 to 75.

65 ≤ x < 75 means that x can take on values from 65 to 74.

Whether it is N or R collection of x elements (where any arbitrary x is 0-dim space) , it does no change the fact that there is always ≠ between any given pair of 0-dim spaces along 1-dim space, which prevents form any amount of 0-dim spaces to completely cover 1-dim space.

epix, you have missed http://www.internationalskeptics.com/forums/showpost.php?p=6474902&postcount=12106 .

 

[zooterkin]

It can't help you to avoid ≠ between some arbitrary distinct pair.

For example: the ...1 of 0.000...1[base 1] is equivalent to ≠ between 0.999...[base 10] and 1, if we avoid mixed bases.

More nonsense. There is no such thing as the ...1, and even if there were, it would not be equivalent to a ≠ sign.

 

[psionl0]

This debate has so far gone on for 304 pages??

G.I.G.O.

 

[The Man]

It can't help you to avoid ≠ between some arbitrary distinct pair.

Who is trying to “avoid ≠ between some arbitrary distinct pair”? Again the fact that the points are not equal means in a continuous space that there is always at least a third point not equal to either of those two between them.

For example: the ...1 of 0.000...1[base 1] is equivalent to ≠ between 0.999...[base 10] and 1, if we avoid mixed bases.

No Doron, as you have been told before your “ ...1” following “0.000...” is just meaningless as “0.000...” represents an infinite series of zeros after the decimal place.


Now if you are trying to claim some non-zero infinitesimal difference between 1 and 0.9999..., then your “points” are no longer zero dimensional, having that non-zero infinitesimal extent.

Wrong. 1-dim space exists independently of any sub-levels of existence along it, where 0-dim space is such sub-level of existence.

OM expresses this notion as 1(0()).

Really? So if the points A and B were equal would your “1-dim space” exist between those points? It is in fact you who are trying “to avoid ≠ between some arbitrary distinct pair” and the dependence of the “1-dim space” on and resulting from that inequality.


Doron, to try to put it more succinctly for you, if “1-dim space exists independently of any sub-levels of existence along it, where 0-dim space is such sub-level of existence” then the “0-dim space” is simply not a “sub-level of” that “1-dim space”. Again if you want that non-zero difference between 1 and 0.999... Then your “sub-level” (your “point“) is simply not a “0-dim space”.

 

[The Man]

This debate has so far gone on for 304 pages??

G.I.G.O.

Indeed, and still evidently just around in circles.

Welcome to the forum and thread psionl0.

 

[epix]

For example: the ...1 of 0.000...1[base 1] is equivalent to ≠ between 0.999...[base 10] and 1, if we avoid mixed bases.

How can 0.000...1 be rendered in number base 1, when the number is made of 2 different digits (zeroes and one)?

See, after your couple of replies that again demonstrate your math illiteracy, I'm not sure if that "base 1" is a typo or not.

 

[epix]

It can't help you to avoid ≠ between some arbitrary distinct pair.

For example: the ...1 of 0.000...1[base 1] is equivalent to ≠ between 0.999...[base 10] and 1, if we avoid mixed bases.

Your notation doesn't allow to visualize both numbers as they approach their limits, as the standard math can. You can't also find the exact point of intersection.

Also, your notation cannot prove that "0.999..." added to "0.000...1" equals 1, as f(x) + g(x) can, coz your notation lacks algebraic terms necessary for the proof.

You need to re-write everything into the standard math language and edit all your posts.

 

[doronshadmi]

Doron if you are trying to claim that two points define a line segment, well, that is exactly what “Traditional Math” and the geometry claims.

“Traditional Math”, which is the reasoning that you are using all along this thread, can't comprehend 1() that is 1-dimensional space with no sub-dimensional spaces along it.

1(0(x) ≠ 0) is a general expression of the concept of Segment, such that any given arbitrary segment 0(x) ≠ 0 is ( non-extendible to 1() ) AND ( irreducible to 0() ).

Once again your assertion that “1() is at AND beyond 0()” simply shows that you can’t even agree with yourself.

Once again your reasoning, where “1() is defined by 0()” simply shows that you can’t comprehend 1() as independent of any sub-spaces.

As e result you have no ability to comprehend 1(0(x)), where 1() is at AND beyond 0(x).

 

[doronshadmi]

See, after your couple of replies that again demonstrate your math illiteracy, I'm not sure if that "base 1" is a typo or not.

The Man, it is a typo, and your poor maneuvers around it simply demonstrate your no-motivation to understand OM.

 

[zooterkin]

The Man, it is a typo, and your poor maneuvers around it simply demonstrate your no-motivation to understand OM.

I think you'll find you are replying to epix, not The Man.

 

[zooterkin]

“Traditional Math”, which is the reasoning that you are using all along this thread, can't comprehend 1() that is 1-dimensional space with no sub-dimensional spaces along it.

Ah, yes, Traditional Math(s), which has given us things such as space travel, computers and many other things we see around us today.

Now, remind me what you can do with OM. Have you yet produced a single example of what use it is? Or even a simple, understandable, example of an expression in it?

 

[epix]

I think you'll find you are replying to epix, not The Man.

Under OM, 1()epix is = AND 1()The Man, and so epix=The Man. Your 0()-only reasoning doesn't allow you to grasp a simple concept.

 

[epix]

Ah, yes, Traditional Math(s), which has given us things such as space travel, computers and many other things we see around us today.

Now, remind me what you can do with OM.

OM application mainly concerns the time travel. Once are the mathematicians able to grasp that "1() that is 1-dimensional space with no sub-dimensional spaces along it," we are right back in the 15th century.

 

[The Man]

“Traditional Math”, which is the reasoning that you are using all along this thread, can't comprehend 1() that is 1-dimensional space with no sub-dimensional spaces along it.

Wrong again Doron, your simply lack of self-consistency and general consistency does not infer that any one lacks comprehension other than you.

1(0(x) ≠ 0) is a general expression of the concept of Segment, such that any given arbitrary segment 0(x) ≠ 0 is ( non-extendible to 1() ) AND ( irreducible to 0() ).

“non-extendible to 1()”? So now your “concept of Segment” isn’t even one dimensional?

Once again your reasoning, where “1() is defined by 0()” simply shows that you can’t comprehend 1() as independent of any sub-spaces.

Well it is not surprising that you simply do not comprehend the meaning of a “sub-space“.

As e result you have no ability to comprehend 1(0(x)), where 1() is at AND beyond 0(x).

Once again Doron your obvious and evidently deliberate lack of self-consistency is entirely comprehensible to everyone but you.

 

[doronshadmi]

Also, your notation cannot prove that "0.999..." added to "0.000...1" equals 1, as f(x) + g(x) can, coz your notation lacks algebraic terms necessary for the proof.

Wrong.

0.999...[base 10]+0.000...1[base 10]=1 has the necessary algebraic terms.

On the contrary the Limit concept does not have the necessary algebraic terms, because it can't explain how a given distinct 0-dimesional space x reaches distinct 0-dimensioanl space y , such that ( there is nothing between 0(x) and 0 ) AND ( 0(x) ≠ 0 ).