Deeper than primes

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The Man said:
Well look who finally caught up. So are you done with your ridiculous claim that “a given line segment is reducible into a point.”?



It’s your utter nonsense Doron, but you may just be catching on to that fact now.
Click to expand...
The utter nonsense is yours, because you are unable to get http://www.internationalskeptics.com/forums/showpost.php?p=6575426&postcount=12371 , which clearly demonstrates this utter nonsense of yours about the sum of convergent lengths, which is = to a given limit.

You are a complete ignorant about this fine subject, because you do not understand the results of your own claims.
 
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doronshadmi said:
The utter nonsense is yours, because you are unable to get http://www.internationalskeptics.com/forums/showpost.php?p=6575426&postcount=12371 , which clearly demonstrates this utter nonsense of yours about the sum of convergent lengths, which is = to a given limit.

You are a complete ignorant about this fine subject, because you do not understand the results of your own claims.
Click to expand...


Referring back to a post where you, Doron, re-demonstrate your lack of understanding of Mathematics doesn't support your claim. The only thing clearly demonstrated in that post is your obstinate insistence on misrepresentation.
 
doronshadmi said:
EDIT:

Let me be clearer about my argument against 1/2+1/4+1/8+1/16+1/32+1/64+… = 1
Click to expand...
That's not the main argument, coz that series approaches it's limit (and according to some even reaches it!) different way than 0.999..., the number that has been expelled from R. You need to look again at
http://www.internationalskeptics.com/forums/showpost.php?p=6563628&postcount=12347
and find the bug there.

There were several UFO sightings years ago that made fun of this particular issue. UFO is 1 acronym divided into 3 letters, so it was predefined as UFO = 1/3. The movement and time of that mysterious triangle in the sky suggested some analogy . . .

1/9 = 0.111...
2/9 = 0.222...
3/9 = 0.333...

Clearly, when the denominator is 9, then the numerator repeats itself infinitely in the result provided by the long division. Since the analogy has formed itself pretty, no need to waste time by dividing -- you just enter the numerator into the result . . .

7/9 = 0.777...
8/9 = 0.888...

When you check once again to make sure that the analogy holds by doing the long division, you find out that the analogy really holds. So let's continue . . .

9/9 = 0.999...

But when you do the long division, then

9/9 = 1

Now it's the analogy vs the long division. Since we've got already enough religious wars, no one needs mathematical wars, and so the elders wisely decided on 0.999... = 1.

So that's the alien contribution to all possible explanation to the miraculous identity. There is another based on the etymology of "long division."

1/3 = 0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333...

Since LOL is 1 acronym divided into 3 letters, LOL = 1/3.
 
zooterkin said:
And what are those locations, exactly?
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From a structural point of view 1/4 (the vertical red line) or 0.01[base 2] have one location along 0________1, where 0.25[base 10] has two locations along 0________1, as follows:

5194100024_c5f8b334f9_b.jpg
 
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doronshadmi said:
From a structural point of view 1/4 (the vertical red line) or 0.01[base 2] have one location along 0________1, where 0.25[base 10] has two locations along 0________1, as follows:

5194100024_c5f8b334f9_b.jpg
Click to expand...

What, you mean one 'location' for 0.2 and one for 0.25? You're kidding, right? In what way is that meaningful or useful? So there would be 3 locations for 1/8 (0.125)? A 'location' is just a decimal place, then? And why is there not one at 0.0 for 0.01[base 2]?
 
zooterkin said:
What, you mean one 'location' for 0.2 and one for 0.25? You're kidding, right?
Click to expand...
I clearly show at least two locations for 0.25[base 10] along 0______1

zooterkin said:
In what way is that meaningful or useful?
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It enables to deal with the structural properties of numbers, in addition to their quantitative properties.

zooterkin said:
So there would be 3 locations for 1/8 (0.125)?
Click to expand...
According to the structural properties of numbers, 1/8 has at least 1 location along 0_____1 and 0.125[base 10] has at least 3 locations along 0_____1

zooterkin said:
A 'location' is just a decimal place, then?
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No, "decimal" is related only to [base 10], where the locations along different scale levels of a given number, can be found in any base value > 1.

zooterkin said:
And why is there not one at 0.0 for 0.01[base 2]?
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It depends on how you define the structural aspect of the number.

If the initial location (0.0) is considered, then 1/4 has at least two locations, which are the initial location 0 AND 1/4 location along 0______1

In that case 1/4 and 0.01[base 2] have two locations along 0______1,
0.25[base 10] has 3 locations along 0______1,
0.125[base 10] hase 4 locations along 0______1, etc ...
 
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doronshadmi said:
From a structural point of view 1/4 (the vertical red line) or 0.01[base 2] have one location along 0________1, where 0.25[base 10] has two locations along 0________1, as follows:

[qimg]http://farm5.static.flickr.com/4087/5194100024_c5f8b334f9_b.jpg[/qimg]
Click to expand...
According to the drawing, you seem to be moving at a constant speed v away from the point of recovery R. . .

Your "correction"
From a structural point of view 1/4 is a single AND strict location along segment 0_______1, where 0.25[base 10] is a non-single AND strict location along 0_______1.
Click to expand...
didn't mention the base 2 nonsensical excuse that you came up with this time.

Theorem: 1 + 1 = 3.

Proof: If we add 1 to 1, we obtain 11, and 11(binary) = 3(decimal).
 
EDIT:

Student: “I have a proof against the assertion that 1/2+1/4+1/8+1/16+1/32+1/64+… = 1, as follows:”

“First, we express 1/2+1/4+1/8+1/16+1/32+1/64+… etc ... by the following diagram:”

________________________________.________________________________ 1/2 +

________________________________________________.________________ 1/4 +

________________________________________________________.________ 1/8 +

____________________________________________________________.____ 1/16 +

______________________________________________________________.__ 1/32 +

_______________________________________________________________._ 1/64 + ...


“If 1/2+1/4+1/8+1/16+1/32+1/64+… = 1, as you assert, then the most right (Red or Blue) segment must be reduced into a single 0-dimensional space.”

“But according to the diagram above, this reduction is impossible, because 1/2+1/4+1/8+1/16+1/32+1/64+… converge as pairs of segments, which have equal lengths , where the values of 1/2+1/4+1/8+1/16+1/32+1/64+… are determined by the most right point of the left segment of any arbitrary convergent pair of Blue\Red Red\blue equal segments, upon infinitely many scale levels”.

“In that case any arbitrary right segment of a given pair of equal segments upon infinitely many scale levels, is exactly the gap between any arbitrary number of 1/2+1/4+1/8+1/16+1/32+1/64+… and the number of the limit.”

Teacher: “Nope, we have been over this before, in order for the current segment being summed to be zero length (a point) the previous sum must already have reached the limit.”

Student: “I agree with you, this reduction is impossible exactly because 1/2+1/4+1/8+1/16+1/32+1/64+… are the most right points of the left segment of any arbitrary convergent pair of Blue\Red Red\blue equal segments, upon infinitely many scale levels”.

“Again, In that case any arbitrary right segment of a given pair of equal segments upon infinitely many scale levels, is exactly the gap between
any arbitrary number of 1/2+1/4+1/8+1/16+1/32+1/64+… and the number of the limit.”

Teacher: “Referring back to your diagram re-demonstrate your lack of understanding of Mathematics doesn't support your claim. The only thing clearly demonstrated in that diagram is your obstinate insistence on misrepresentation.”

Student: “Is this kind of reply is considered by you as a reasonable answer to my proof against
the assertion that 1/2+1/4+1/8+1/16+1/32+1/64+… = 1?”

“Since you assert that 1/2+1/4+1/8+1/16+1/32+1/64+… = 1, then please show it without reducing the most right (Red or Blue) segment into a single 0-dimensional space.”
 
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epix said:
n the base 2 nonsensical excuse that you came up with this time.

Theorem: 1 + 1 = 3.

Proof: If we add 1 to 1, we obtain 11, and 11(binary) = 3(decimal).
Click to expand...
Wrong theorem, because 0______1 is independent of any base value, as clearly shown by the following diagram:

5194100024_c5f8b334f9_b.jpg
 
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doronshadmi said:
Student: “I have a proof against the assertion that 1/2+1/4+1/8+1/16+1/32+1/64+… = 1, as follows:”

“First, we express 1/2+1/4+1/8+1/16+1/32+1/64+… etc ... by the following diagram:”

________________________________________________________________ 1/2 +

________________________________________________________________ 1/4 +

________________________________________________________________ 1/8 +

________________________________________________________________ 1/16 +

________________________________________________________________ 1/32 +

________________________________________________________________ 1/64 + ...


“If 1/2+1/4+1/8+1/16+1/32+1/64+… = 1, as you assert, then the most right (Red or Blue) segment must be reduced into a single 0-dimensional space.”

“But according to the diagram above, this reduction is impossible, because 1/2+1/4+1/8+1/16+1/32+1/64+… converge as pairs of segments, which have equal lengths , where the values of 1/2+1/4+1/8+1/16+1/32+1/64+… are determined by the most right point of the left segment of any arbitrary convergent pair of Blue\Red Red\blue equal segments, upon infinitely many scale levels”.

“In that case any arbitrary right segment of a given pair of equal segments upon infinitely many scale levels, is exactly the gap between any arbitrary number of 1/2+1/4+1/8+1/16+1/32+1/64+… and the number of the limit.”

Teacher: “Nope, we have been over this before, in order for the current segment being summed to be zero length (a point) the previous sum must already have reached the limit.”

Student: “I agree with you exactly because 1/2+1/4+1/8+1/16+1/32+1/64+… are the most right points of the left segment of any arbitrary convergent pair of Blue\Red Red\blue equal segments, upon infinitely many scale levels”.

“Again, In that case any arbitrary right segment of a given pair of equal segments upon infinitely many scale levels, is exactly the gap between
any arbitrary number of 1/2+1/4+1/8+1/16+1/32+1/64+… and the number of the limit.”

Teacher: “Referring back to your diagram re-demonstrate your lack of understanding of Mathematics doesn't support your claim. The only thing clearly demonstrated in that diagram is your obstinate insistence on misrepresentation.”

Student: “Is this kind of reply is considered by you as a reasonable answer to my proof against
the assertion that 1/2+1/4+1/8+1/16+1/32+1/64+… = 1?”
Click to expand...

http://en.wikipedia.org/wiki/Schizophrenia
 
doronshadmi said:
...
Click to expand...


Someday, just maybe, you'll repeat this nonsense, and it will suddenly and magically become true. It will cease to be a gross misrepresentation and misunderstanding on your part.

Today, however, is not that day. You are still blatantly, embarrassingly wrong.
 
Doron,
Here, let's give you a leg-up on that "someday." All you need do is disprove the following statement. Then that nasty old summation won't work any more.

[latex]$$$\displaystyle
\forall {\epsilon > 0} ,\: \exists N \; n > N \Rightarrow \epsilon > \left| 1 - \sum_{i=1}^{n} {1 \over {2^i}} \right|
$$$[/latex]​

Perhaps you can find a simple counter example?
 
doronshadmi said:
The utter nonsense is yours, because you are unable to get http://www.internationalskeptics.com/forums/showpost.php?p=6575426&postcount=12371 , which clearly demonstrates this utter nonsense of yours about the sum of convergent lengths, which is = to a given limit.

You are a complete ignorant about this fine subject, because you do not understand the results of your own claims.
Click to expand...


Nope, I have certainly never claimed “a given line segment is reducible into a point.”. That ridiculous and utterly nonsensical claim is just yours Doron. That you would simply like to ascribe it to others does not make it any less your own utter nonsense. You are completely and evidently deliberately ignorant since you just don’t want to comprehend that the results of your claims are still just the results of your claims, regardless of whom you whish to ascribe them to.
 
"Of Cardinality"

Sung to the tune of

"AT SEVENTEEN" By Janis Ian





"Of Cardinality"

I learned the truth of cardinality
That mathematicians just can’t see
Among existing things with some magnitude
Of values to which I’ll just allude
The concepts that I never knew
The musing of kindergarten youth
Were taken as demonstrable
Of cardinality I learned the truth...

And those of us with 1-D spaces
Just can’t cover all the places
With just points all alone
Imagining math of my own
Replete with inconsistencies
And repeated vague obscurities
It isn't all it seems, of cardinality...

It’s from Fullness that it all abounds
For any non-empty set around
By some vague non-local property
I’ll claim with all sincerity
The set exists beyond itself
and add to it my imagination’s wealth
With even more obscurity
A linkage called complexity...

So remember those who use a set
And haven’t got that linage yet
From claims lacking quality and dubious integrity
I’ll ascribe to them claims of my own design
And unflinchingly claim a line
Exceeds the points it has, in cardinality...

From Emptiness we still must gain
The explanation that never came
Of the linkage from which it all ensues
You don’t get it? Well you lose
That’s too bad, it just a shame
If I can’t explain, it’s just you I’ll blame
Your direct perception just can’t see
This linkage of complexity…

It’s a fantasy that’s just repeated
An infinite set can’t be completed
With it’s members all alone
Imagining math of my own
Replete with inconsistencies
And repeated vague obscurities
It just isn't anything, of cardinality...
 
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