Deeper than primes

[doronshadmi]

I was right in my suspicion that you don't have the vaguest idea about the concept of points. If there is a location on 1-dim object, such as the initiator line of the Koch curve, that a point cannot define, then you can't "cut and bend" the line infinitely. That's because for that activity you need to locate the vertex and the inflection points. Any modification or a construction of objects with d>0 requires the presence of defining points, and you are totally oblivious to that fact. You only see that after one million iterations, the Koch curve still comprise combination of line segments and points and therefore there would be always a point-line-point segment, e.g. there would be always a space between two points "not covered by a point." But after another couple of million iterations you find that this particular line segment is littered with vertex points as the bending continues. Go back and look at the example once again. Do you see any other point apart from the endpoints?

O_____________________M

No?
The conclusion is then that this line segment is not entirely covered by points. That also means that this line segment can't become the generator of the Koch curve, coz you can't locate the necessary inflection and vertex points to modify the line. The reason why you can't locate the points is the absence of any points between O and M. That in turn means that the finite length of the O_M line cannot be divided by number 3, coz the result of such a division looks like

O_______|_______|_______M

and since there are no points between O and M, there is no way to define and locate the points through (M - O)/3. The general consequence is that Organic Mathematics discovered numbers greater than zero that are indivisible. (Applause.)

BUT! The concept of the limit says that there is always a space between two points on a curve, otherwise there would be no derivative of the function that draws such a curve, and without us being able to compute derivatives, the science time would stop in the 16th century. The length of such a pointless segment approaches zero -- zero is the limit. So in this respect, it's true that "line cannot be entirely covered by points." On the other hand, any line length can be further divided. That's a contradiction that the concept of infinity solves. You can locate any point on a curve and at the same time compute the derivative of the function that draws the curve. The result in the approximate format would be "infinitely precise," but not "exact."

epix this is the second time that you agree with OM and does not agree with Traditional Math ( the first time was in http://www.internationalskeptics.com/forums/showpost.php?p=6518481&postcount=12211 ), because Tradisional Math claims that a 1-dim space is totally covered by 0-dim spaces, such that 1/2+1/4+1/8+1/16+... = EXACTLY 1, where 1 is the limit.

PI is to EXACT as 3.1415... is to INFINITELY PRECISE

In other words, Do you agree that 3.1415...[base 10] < PI , as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6470162&postcount=12091 ?

Please answer to this question only by "Yes" or "No".

 

[epix]

epix this is the second time that you agree with OM and does not agree with Traditional Math ( the first time was in http://www.internationalskeptics.com/forums/showpost.php?p=6518481&postcount=12211 ), because Tradisional Math claims that a 1-dim space is totally covered by 0-dim spaces, such that 1/2+1/4+1/8+1/16+... = EXACTLY 1, where 1 is the limit.

Show me any text that says 1/2 + 1/4 + 1/8 + 1/16 + ... = 1. You never provide any evidence of what you think mathematicians claim. It's very possible though that you'd come across that expression in the form of

∞
∑ 1/2^k = 1
k=1

where the writer assumes that the infinity symbol above Sigma is a sufficient indication of 1 being the limit of the sum and not its exact result and skips the lim k → ∞ before Sigma.

It's remarkable to find out that you've brainwashed yourself into the state of irreversible belief about mathematicians being that stupid to believe that 1 + 2 + 3 + 4 + ... = "exact result".

In other words, Do you agree that 3.1415...[base 10] < PI , as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6470162&postcount=12091 ?

Please answer to this question only by "Yes" or "No".

No. According to OM, 0.999... = 1 (exact result).

0.999... = 0.9 + 0.09 + 0.009 + ... + 0.000...1 = 1

http://www.internationalskeptics.com/forums/showpost.php?p=6514794&postcount=12201

and therefore 3.1415... = Pi and not 3.1415... < Pi

You can't have it both ways, Doron. Just make up your mind and let me know when that happens.

How is that instrument that will multiply very small but finite numbers for OM going along? Are you finished devising or not? You can't collapse the world of traditional mathematics and render it no good without showing that the axe that went down knows how to multiply all numbers that live in R.

 

[doronshadmi]

No. According to OM, 0.999... = 1 (exact result).

0.999... = 0.9 + 0.09 + 0.009 + ... + 0.000...1 = 1

Wrong conclusion since (0.999...[base 10] = 0.9[base 10] + 0.09[base 10] + 0.009[base 10] + ...) < (0.9[base 10] + 0.09[base 10] +
0.009[base 10] + ... + 0.000...1[base 10] = 1) by 0.000...1[base 10]

Show me any text that says 1/2 + 1/4 + 1/8 + 1/16 + ... = 1. You never provide any evidence of what you think mathematicians claim.

It is not what I think and this is exactly what Traditional Math claims about the considered subject, for example:

Here is an evidence about 1/2 + 1/4 + 1/8 + 1/16 + ... = 1, according Traditional Math:

http://en.wikipedia.org/wiki/1/2_+_1/4_+_1/8_+_1/16_+_·_·_·

http://en.wikipedia.org/wiki/Absolute_convergence

Here is an evidence about 0.999... = 1, according Traditional Math:

http://en.wikipedia.org/wiki/0.999...

It's remarkable to find out that you've brainwashed yourself into the state of irreversible belief about mathematicians being that stupid to believe that 1 + 2 + 3 + 4 + ... = "exact result".

On the contrary, OM claims that 1 + 2 + 3 + 4 + ... = "does not have an exact result"

Furthermore, OM claims that the cardinality of infinitely many distinct things "does not have an exact result", where Traditional Math (according to Cantor's reasoning) claims that the cardinality of infinitely many distinct things "has an exact result", like aleph0, 2^aleph0 , etc. ...

 

[doronshadmi]

By the way, here is a nice program of Ford circles zoom in-out:

http://nrich.maths.org/public/viewer.php?obj_id=6594&part=index

 

[epix]

It is not what I think and this is exactly what Traditional Math claims about the considered subject, for example:

Here is an evidence about 1/2 + 1/4 + 1/8 + 1/16 + ... = 1, according Traditional Math:

http://en.wikipedia.org/wiki/1/2_+_1/4_+_1/8_+_1/16_+_·_·_·

http://en.wikipedia.org/wiki/Absolute_convergence

Here is an evidence about 0.999... = 1, according Traditional Math:

http://en.wikipedia.org/wiki/0.999...

That's not what traditional math claims; that's what pseudo mathematicians claim. Just look at the animated "informal proof" of the series in question. That's a complete joke. There are two kinds of professionals: those who know and those who understand. An appeal to authority obscures the distinction.

If you stick with the particular subject, then you find out that not all is well with the world of mathematics. Fortunately, certain "irregularities" occur as stuff is approaching infinity, and therefore there is no physical representation.

Look at this case: If you organize all real numbers in the ascending order, then the result can be very much likened to a line segment "completely covered by points." That includes numbers, such as a < 1, with one digit repeating after the radix ad infinitum. An example of such a number is

0.999...

Does such a number exist?

According to 0.999... = 1 that the Wiki contributor and others love so much, such a number doesn't exist and therefore the line R cannot be entirely covered by points, as OM says.

There is an algorithm called "long division." You need to put that under the magnifying glass. It starts with

1/3 = 0.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333

How about inventing an expression that would indicate that nothing is going to change above? How about

1/3 = 0.333... ?

That leads to taking a close look at terms such as "exact" and "approximate." The initial proof of 0.999... = 1 relies on 1/9 = 0.111... Is it really so?

 

[doronshadmi]

That's not what traditional math claims;

It is exactly what traditional math claims.

According to 0.999... = 1 that the Wiki contributor and others love so much, such a number doesn't exist and therefore the line R cannot be entirely covered by points, as OM says.

1) OM says that R is an incomplete collection of 0() dimensional spaces, which can't entirely cover 1() dimensional space.

2) OM says that accordinng to (1) there exists number 0999...[base 10] < 1 by number 0.000...1, where the ...1 part of 0.000...1 expresses the 1() dimensional spaces that is not covered by 0() dimensional spaces.

3) Traditional Math claims that 0.999...[base 10] is one of many other numerals that represent number 1, exactly because Traditional Math claims that 1() dimensional space entirely covered by points (by 0() dimensional spaces ).

 

[laca]

Hey doron, sorry to barge in after so long, but any luck in publishing anything? No? Still no, after all those years? What's it been now, 10? Aw, sorry. But don't despair! Maybe, just maybe, if you keep it up long enough, you get a nice white jacket as a consolation prize. With sleeves!

 

[doronshadmi]

Hey doron, sorry to barge in after so long, but any luck in publishing anything? No? Still no, after all those years? What's it been now, 10? Aw, sorry. But don't despair! Maybe, just maybe, if you keep it up long enough, you get a nice white jacket as a consolation prize. With sleeves!

Hey laca. Maybe, just maybe, if you keep it up long enough, your black tooth in your mouth will fall by itself, and you will be able cancel your appointment with your dentist and save the money for your shrink.

You can take epix with you if you fill lonley.

 

[laca]

Hey laca. Maybe, just maybe, if you keep it up long enough, your black tooth in your mouth will fall by itself, and you will be able cancel your appointment with your dentist and save the money for your shrink.[qimg]http://farm2.static.flickr.com/1182/5154460003_f71d498947_t.jpg[/qimg]

Oh, I've struck a nerve, haven't I?

You can take epix with you if you fill lonley.

I'm not sure what lonley is or how to fill it... Maybe you can enlighten me? Oh, wait...

But seriously, doron. Can you answer a few questions for me?

1. How much is 9/9?
2. How about 99/99?
3. 7/9?
4. 76/99?
5. n/9, where n <= 9

Now tell me, how much is 0,999....?

 

[epix]

It is exactly what traditional math claims.
Here is an evidence about 1/2 + 1/4 + 1/8 + 1/16 + ... = 1, according Traditional Math:

http://en.wikipedia.org/wiki/1/2_+..._·_·

http://en.wikipedia.org/wiki/Absolute_convergence

Your concept of evidence is based on a singular appeal to authority, even though in your case it's kind of different, coz you have taken on the traditional math armed with nothing but a snow ball.

Let's take a look at what traditional math has to say about the absolute convergence that is particular to the conclusion about the result of the sum:

In mathematics, a series (or sometimes also an integral) of numbers is said to converge absolutely if the sum (or integral) of the absolute value of the summand or integrand is finite.

http://en.wikipedia.org/wiki/Absolute_convergence

A series [symbol] is said to converge absolutely if the series [symbol] converges, where [symbol] denotes the absolute value. If a series is absolutely convergent, then the sum is independent of the order in which terms are summed. Furthermore, if the series is multiplied by another absolutely convergent series, the product series will also converge absolutely.

http://mathworld.wolfram.com/AbsoluteConvergence.html

You see that the quote from Eric Weisstein at Wofram Research never mentions what Wiki claims about the finite sum. That's because not too many folks are capable of such an aggravated assault on common sense and grossly misdefine the meaning of the term "absolute convergence." Can't you understand that Wikipedia is a public encyclopedia and any idiot can edit it?

 

[doronshadmi]

Oh, I've struck a nerve, haven't I?

Yes, the nerve of your black tooth.

 

[laca]

Yes, the nerve of your black tooth.

Yeah, yeah. So, no answer? Come on, a man of your intellect can surely answer a couple of simple questions! You do remember how to do divisions from elementary school, don't you?

 

[doronshadmi]

Can't you understand that Wikipedia is a public encyclopedia and any idiot can edit it?

Here is more stuff about this subject, according to Traditional Math:

http://www.math.toronto.edu/mathnet/questionCorner/geomsum.html

 

[The Man]

The Man you have no case because you do not distinguish between the complex and the non-complex.

Doron “you have no case because you do not distinguish between” your fantasies and misconceptions (often apparently deliberate) from, well, mathematics.

Your dichotomist labels do not change the fact that a space is not independent of its sub-spaces.

You are talking about the dependency under the complex results among independent spaces.

No Doron I’m specifically talking about that fact that a space is not independent of its sub-spaces. That you simply want to talk about something else, once again your dichotomist labels, is simply your problem.

Let me give you an example:

The existence of 1-dim and 0-dim spaces are independent of each other, such that if one of them is missing, the other one still exists.

Once again a space is not independent of its sub-spaces, which, for a “1-dim” space, includes both “1-dim” and “0-dim spaces” as sub-spaces of that space. While a point, being zero dimensional, has no sub-spaces.

Now let's observe a complex like line-segment, which is the result of the linkage among 1() and 0().

“the result of the linkage among 1() and 0().” makes your “complex like line-segment” dependent on both Doron, by your own assertion.

Even if the length of 1() space under the complex, called line-segment, depends on the values of 0() spaces, it does not mean the 1() or 0() existence depend on each other.

Again, simply repeating your nonsense assertions from before does not change the fact that a space is not independent of its sub-spaces.

 

[laca]

Hey, doron! Still no luck with that elementary math? Here it is again:

But seriously, doron. Can you answer a few questions for me?

1. How much is 9/9?
2. How about 99/99?
3. 7/9?
4. 76/99?
5. n/9, where n <= 9

Now tell me, how much is 0,999....?

If you want to, I could refresh your memory on how to do divisions.

 

[doronshadmi]

“1-dim” space, includes both “1-dim” and “0-dim spaces” as sub-spaces of that space.

In other words, you show again your inability to distinguish between

∞(
1(),0()
)

and

∞(
1(0())
)

because you are a Total L0()ss case.

 

[laca]

We can play this game too if you wish.

You can't get 9/9. Ha!

 

[epix]

Here is more stuff about this subject, according to Traditional Math:

http://www.math.toronto.edu/mathnet/questionCorner/geomsum.html

This time the traditional math is doing a good job explaining stuff to a 12th grader:

... and this sequence of numbers (1, 3/2, 7/4, 15/8, . . . ) is converging to a limit. It is this limit which we call the "value" of the infinite sum.

Note that the writer put the word value into the quotation marks. If you wonder why, follow the yellow line . . .

The writer didn't use the informal and strongly intuitive proof that the sum of the sequence in question is converging toward 2 but never reaches the number, as it obviously can't, but in this circumstance, let's refresh it using the original sequence you argued about that starts with 1/2.

1/2 = 1/2
1/2 + 1/4 = 3/4
1/2 + 1/4 + 1/8 = 7/8
1/2 + 1/4 + 1/8 + 1/16 = 15/16
1/2 + 1/4 + 1/8 + 1/16 + 1/32 = 31/32

You can see that the result of the partial sums have always the form (denominator-1)/denominator, and this configuration will not change as there will be more and more addends whose number will be approaching infinity. In other words, there will never be a moment where suddenly the partial result of the sum will change into numerator = denominator with the result of exact 1.

It's very hard to believe that the "traditional mathematicians" would fail to ponder this kind of development and propose that the "result of the sum is exactly 1."

 

[The Man]

In other words, you show again your inability to distinguish between

∞(
1(),0()
)

and

∞(
1(0())
)

because you are a Total L0()ss case.

Once again you simply show your inability to understand that a space is not independent of its sub-spaces.

 

[epix]

Here is more stuff about this subject,