Back to the gibberish, I see.
Deeper than primes
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Back to the gibberish, I see.
doronshadmi
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Never gives up of ignorance, I see.
doronshadmi
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Epix, you can use any function that you wish.
It does not change the fact that there is ≠, which exists between any given arbitrary pair of distinct exact locations (arbitrary pair of distinct points) that are the strict results of the given function.
≠ is definitely free of any strict results, which gives it the ability to be used both as differentiator AND integrator of the concept of Pair.
Without, for example, 1(0(x)≠0
) there is no pair.
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Who says that it isn't so? Any xi that is a part of R is distinct, such as xi-1 < xi < xi+1. That's why you can see a line. You claim that point [x = 2, y = 4] doesn't have an exact location. Did you hack the Hubble telescope and see something not round "at the end" of 2.000... and 4.000...?
Eventually, there has to be point p > 2 that you express as p = 2.000...1. That means the "strict" number 2 is not immortal. Or is it?
You are applying your everyday experience into an abstract world that is not physical, and that creates a conflict. But that's normal:
a4 = a * a * a * a
a3 = a * a * a
a2 = a * a
a1 = a
a0 = ?
a0 seems to be the same case as a/0.
12/4 = 12 - 3 - 3 - 3
12/3 = 12 - 4 - 4
12/2 = 12 - 6
12/1 = 12
12/0 = ?
Both analogies are not identical, as far as the result is concerned, even though your intuition tells you that they are.
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doronshadmi
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Wrong, 1(0(2)≠0(4)) is 1() (notated by ≠) between strict numbers.
2.000...1() is a non strict number (where the concept of Number is a measurement tool, whether the measured is a strict or non-strict level of existence or a given strict or non-strict location), for example:
0(2) is a valid expression, 0(2.000...1) is an invalid expression, 2.000...1(0(2)) is a valid expression.
Again, the general form is X(x), where X is strict or non-strict level of existence, and x is strict or non-strict location, such that X=0 has only strict locations (also X=0 does not have sub-levels of existence), and X>0 has (strict OR non-strict locations) OR (strict OR non-strict sub-levels of existence).
No, 0 < a0 = 1 < a/0 = ∞ < ∞
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Arbitrary points are not "the strict results of the given function," as they cannot be given their definition. The result of a given function is not an arbitrary point -- that point is defined by the function. An arbitrary point is the independent variable, and the value of the dependent variable... well, depends on the way the independent variable is treated by the function f(x). In other words, f(x) = y, where x is the independent, or arbitrary, variable and y is the dependent variable. So, for x = 2, the function
f(x) = (x2 - 4)/(x - 2) = 0/0
and the corresponding dependent variable y doesn't exist on the y-axis, coz the function doesn't define it (division by zero). That means there can't be no point drawn on the line that visualizes the f(x) = y relationship. Remember that integer 2 and real number 2 are not the same: in the latter case, 2 is a short for 2.000.... Unlike in a = 2.333... where a is approaching limit 7/3, the integers of real numbers are not approaching any limit and are therefore exact numbers.
2.33333 - 2.333 > 0
but
2.00000 - 2.000 = 0
That's why there is one and only one point missing in the straight line that represents the function f(x) above and that's why algebra uses fractional representation of non-integer numbers, which is the limit.
Since OM doesn't recognize the function as an instrument that graphically displays values of the modified independent variable, there is no way to prove that assertions made by OM are true or false.
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The Man
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So then there are no locations on your line that are not or can not be covered by points as you assert “any given exact location” is a point.
Again, stop simply trying to posit aspects of your own failed reasoning onto others.
You can stop any time. Or can you?
“≠” still isn’t a location Doron and you simply inserting “exact” and “non-exact into your dichotomist terminology doesn’t change that.
Please identify any location “between any given arbitrary pair of distinct exact locations (arbitrary pair of distinct points)” that is not or can not be covered by points.
doronshadmi
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Again,
Traditional Math can't comprehend that ≠ is the non-local property of 1() w.r.t 0(), such that ≠ is the existence of 1() between any given arbitrary pair of distinct 0() ( as expressed by 1(0(x)≠0
) ), or simply the fact that 1() is at AND beyond 0() ( as expressed by 1(0()) ). ≠ is definitely free of any 0(), which gives it the ability to be used both as differentiator AND integrator of the concept of 1(0(x)≠0
) Pair.Moreover, Traditional Math's claim that 1() is completely covered by 0() is equivalent to the claim that (for example) variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0, which is definitely a contradiction.
The Man, your 0()-only reasoning is too weak in order to deal with 1(0()) or 1(0(x)≠0
).You can write as many replies as you wish, which does not change the fact that you are closed under 0()-only reasoning, which is weaker than 1(0()) reasoning.
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Again,
Traditional Math can't comprehend that ≠ is the non-local property of 1() w.r.t 0(), such that ≠ is the existence of 1() between any given arbitrary pair of distinct 0(), which expressed as 1(0(x)≠0
≠ is definitely free of any 0(), which gives it the ability to be used both as differentiator AND integrator of the concept of 1(0(x)≠0
Moreover, Traditional Math's claim that 1() is completely covered by 0() is equivalent to the claim that (for example) variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0, which is definitely a contradiction.
So, you still can't identify a location on a line where there is no point? Got it. Do you think you could stop claiming that you can?
doronshadmi
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You are simply still missing the fact that f(x) is equivalent to 1(0()), such that f() is equivalent to 1() and x (if it is strict) is equivalent to 0().
Wrong, 2 or 2.000... is exactly the same 0().epix said:
You are still missing 2.000...1(0(2)), such that 2.000...1() - 0(2) = 0.000...1(), which can be expressed as 2.000...1(0.000...1())
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doronshadmi
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So, you can't comprehend 1(0()) or 1(0(x)≠0
)! Got it.Do you think you could stop claiming that (for example) variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0, which is definitely a contradiction?
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This is the reason why OM cannot display its own version of a f(x) graph, coz the definitions, based on the OM terminology, are the insurmountable obstacle. The traditional math understands that f() doesn't make sense without the indication which independent variables are to be modified by the function, and so f() never appears in the text, except in the case of non-mathematical applications where f() may substitute the traditional f... as a brief comment that summarizes certain unexpected outcomes.
In OM, f() = 1() means that a function without independent variables equals a one-dimensional space
confused. You decided to notate a one-dimensional space as 1(), coz you didn't worry about a possible conflict with f(x), coz you never use it. Following the meaning of 1(), it's inevitable that f() implies an f-dimensional space and not a function where the independent variable(s) are not present. I think you need to come up with correcting syntax ideas and edit all the posts that you have written.
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I didn't refer to the value of 2 and 2.000... Just read again.
Your conclusion is contradictory by itself and the reason is that you can't still grasp the meaning and the usage of intervals despite all the explaining links provided.
Suppose that an insurance analyst wants to know the probability that a person dies due to a specific illness between the age of 65 and 75 including, where the age of the person upon expiring is defined as X. He collects sample data, does some number crunching and finds out that the probability P is
P(65 ≤ X ≤ 75) = .68 [68%]
That person who gets unlucky doesn't die twice at the age of 65 and 75; it dies only once in the age that is within the range indicated. That person dies only once, coz he or she lives only once. Just don't get confused by some high-powered theoretical claims based on the latest research in genetics done by Prof. Sinatra.
doronshadmi
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In OM X() is a level of strict of non-strict existence, which exists independently of any sub-levels. X can be number, function, dimensional space, or any measurable strict or non-strict level of existence.In OM, f() = 1() means that a function without independent variables equals a one-dimensional space
You still do not get the generalization of X(), such that a given X's existence is independent of any other given X.
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doronshadmi
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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, whether the previous levels are non-strict ( like 0.999...[base 10]() ) or strict ( like 0(x) ).
You are still missing, for example: 1(0.999...[base 10]()), 1(0(x)≠0
), 0.999...[base 10](0(x)), etc ...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
epix, you can't grasp that strict 0(x) value can't be = AND ≠ to strict 0
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.
The Man
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Again,
Traditional Math can't comprehend that ≠ is the non-local property of 1() w.r.t 0(), such that ≠ is the existence of 1() between any given arbitrary pair of distinct 0() ( as expressed by 1(0(x)≠0
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.
Once again your assertion that “1() is at AND beyond 0()” simply shows that you can’t even agree with yourself.
≠ is definitely free of any 0(), which gives it the ability to be used both as differentiator AND integrator of the concept of 1(0(x)≠0
Once again Doron, “≠“ is simply an assertion of inequality. However, in a continuous space there is always at least another point between any two points.
Again please identify any location(s) on a line segment that is not and can not be covered by points.
No Doron your continued misrepresentation of the symbols “≤ “ “≥” only makes your claim “equivalent” to your own misrepresentation.
To try to clarify it again for you, any point included in the interval [0,1] is > 0 AND < 1, OR = 1, OR = 0. Your “both ≤ 1 OR both ≥ 0” claim is just nonsense and only shows that you do not understand the “≤” and “≥” symbols. “Both” < OR = (“both ≤ “) as well as “both” > OR = (“both ≥”) is a contradiction and it remains simply yours.
The Man, your 0()-only reasoning is too weak in order to deal with 1(0()) or 1(0(x)≠0
You can write as many replies as you wish, which does not change the fact that you are closed under 0()-only reasoning, which is weaker than 1(0()) reasoning.
Again, stop simply trying to posit aspects of your own failed reasoning onto others.
The Man
Unbanned zombie poster
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?
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.epix, you can't grasp that strict 0(x) value can't be = AND ≠ to strict 0
In other words, no given level of existence is completely covered by any collection of previous levels of existence.
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) = [(
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.
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doronshadmi
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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.
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 ).
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
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doronshadmi
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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.
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doronshadmi
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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.
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doronshadmi
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Wrong. 1-dim space exists independently of any sub-levels of existence along it, where 0-dim space is such sub-level of existence.epix said:
OM expresses this notion as 1(0()).
doronshadmi
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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 .
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More nonsense. There is no such thing as the ...1, and even if there were, it would not be equivalent to a ≠ sign.
psionl0
Skeptical about skeptics
This debate has so far gone on for 304 pages??
G.I.G.O.
G.I.G.O.
The Man
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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.
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.
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
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Indeed, and still evidently just around in circles.
Welcome to the forum and thread psionl0.
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.
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.
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doronshadmi
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“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.The Man said:
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() ).The Man said:
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
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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.
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?
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.
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
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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
“non-extendible to 1()”? So now your “concept of Segment” isn’t even one dimensional?
Well it is not surprising that you simply do not comprehend the meaning of a “sub-space“.
Once again Doron your obvious and evidently deliberate lack of self-consistency is entirely comprehensible to everyone but you.
doronshadmi
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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 ).- Status