Deeper than primes

[punshhh]

"Atom" is one of many terms Doron uses with no regard to their actual meanings. It is certainly not being used in this thread by anyone in the sense of a physical particle, nor are we discussing the Big Bang. You seem to be going off on a tangent entirely of your own.

(You might want to check that your keyboard is working, you seem to be losing characters. (Planck, epoch, for example.))

Thanks

I was using an example to illustrate that I understood the argument.

There is little more I can say regarding the argument itself.

 

[zooterkin]

I was using an example to illustrate that I understood the argument.

I think it's fair to say you did illustrate your understanding of the argument.

 

[doronshadmi]

So infinity in base 2 is five times as big as infinity in base 10?

0.000...1[base 2] > 0.000...1[base 10] according to the ratio between 1/2 and 1/10.

As a result 0.999...[base 10] is closer to 1 than 0.111...[base 2]

In order to understand it please see the difference between 0.111...[base 2] and 0.222...[base 3] , according to the following diagram:

 

[doronshadmi]

"Atom" is one of many terms Doron uses with no regard to their actual meanings. It is certainly not being used in this thread by anyone in the sense of a physical particle, nor are we discussing the Big Bang. You seem to be going off on a tangent entirely of your own.

Again.

A point is exactly the smallest possible element.

A line segment is "at its best" an ever smaller element, which logically can't be reduced into the smallest possible element.

This reasoning is consistent, straightforward and easily understood by any open mind person.

The reasoning that can't get that is used by persons that do not have open minds, which is the majority of the current community of pure mathematicians that have no clue about the real complexity of the co-existence of the ever smaller AND the smallest.

 

[zooterkin]

0.000...1[base 2] > 0.000...1[base 10] according to the ratio between 1/2 and 1/10.

As a result 0.999...[base 10] is closer to 1 than 0.111...[base 2]

In order to understand it please see the difference between 0.111...[base 2] and 0.222...[base 3] , according to the following diagram:

[qimg]http://farm3.static.flickr.com/2793/4318895416_e5d2042b0c_z.jpg?zz=1[/qimg]

I didn't ask about your imaginary construction 0.000...1, I asked about infinity. And zero is still zero whichever base it is in.

 

[zooterkin]

Again.

A point is exactly the smallest possible element.

Well, given that it has zero size, it couldn't be any smaller.

A line segment is "at its best" an ever smaller element, which logically can't be reduced into the smallest possible element.

Could you reword that to be in English?

This reasoning is consistent, straightforward and easily understood by any open mind person.

No, it isn't. It's not possible to see what you mean, so we can't tell if it makes sense (though I know which way I'd bet).

 

[doronshadmi]

I asked about infinity.

And I gave an answer about the infinitely smaller, which is irreducible into the smallest possible element.

And zero is still zero whichever base it is in.

Also as 1 is 1, no matter what base value is used, exactly as shown in the following diagram:

 

[doronshadmi]

Could you reword that to be in English?

Could you reword your mind in order to get the ever smaller, which is logically irreducible to the smallest?

 

[jsfisher]

Could you reword that to be in English?

Could you reword your mind in order to get the ever smaller, which is logically irreducible to the smallest?

I'll take that as a "no".

 

[epix]

Could you reword your mind in order to get the ever smaller, which is logically irreducible to the smallest?

I thought you would be interested in that YouTube demonstration of creating a curve by drawing some of its slopes. Combined with "real math," it shows that a line segment whose length is approaching zero can be regarded as a point. That YouTube video treats the construction as an optical effect, but I did a short follow up. You draw two Cartesian co-ordinates both 10 units long and divide them on equidistant segments 1 unit in length and then connect the points as shown bellow.

The connecting lines create a near curve, which is a collection of ten straight lines where the red points are the points of intersection of the slope lines that lie on the curve. Since the curve is a collection of measurable straight lines, it's easy to estimate the length of the curve when it becomes smooth by simply measuring the distances from point to point and adding them together.

Measured combined length = 15.885793

In order to smooth the curve, you don't really need to divide both coordinates on many more segments -- a fairly simple use of parametric equations will utilize the coordinates of the red points, so you can derive the function of the curve. You can see the function that draws the curve that is now "infinitely smooth" bellow.

The function of the curve is equivalent to the procedure where you divide both coordinates on infinitely many segments and repeat the construction above, which is hardly possible. But the division establishes the length of each segment on the coordinates.

[lim n → ∞] 10/n = 0

The above tells you that the length of each line segment is approaching zero and you are free to treat each segment as a point. The same goes for the curve, which is now a collection of line segments whose number is approaching infinity. All you need to do is to measure each segment and add them together to get the length of the curve. That's not really possible, coz the number of those line segments is infinite. But there is that "Mathew Theorem":

Theorem 19:26
Jesus looked at them (it) and said, “With man this is impossible, but with God all things are possible.”

And so you need to integrate:

Length of the curve = √2 ₀ ∫¹⁰√ ((-22 (√ (44x + 1) + 44x +243)/(44x + 1)) dx = 15.900219...

Now compare the computed length whose precision is approaching infinity with the measured length, which was 15.885793. Not much of a difference, is it?

Point #1 is that you can't compute the length of a curve without defining it and treat it as a collection of line segments whose number is approaching infinity where the length of each segment is approaching zero.

Point #2 is that solving problems may require special definition and treatment of the objects that the problem is made of to get the job done. The mathematicians in the beginning of the 20th century attempted to put math "under one God" but Kurt Godel, that is Kurt GODel, showed them that it wasn't possible. And that's my contribution to the fallacies in the Bible by disproving the already mentioned "theorem":

Jesus looked at them (it) and said, “With man this is impossible, but with God all things are possible.”
Mathew 19:26

In 1926 he transferred to mathematics and coincidentally became a member of the M. Schlick circle.

http://www.jstor.org/pss/2273764

Wow! That's pretty good, "heavenly father." Keep manipulating and don't forget to send down some more stuff... LOL.

Cantor believed his theory of transfinite numbers had been communicated to him by God

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

CANtor GODel TEACH MATH?

The rational dogma of the 21st century says, "no way!"

 

[laca]

Really laca, science tells us that all the atoms (points) where present in one point (singularity), at or slightly before the Planck epoc during the big bang.

Do explain what atoms got to do with infinite regress and the fact that 0.(9) equals exactly 1.

We have a vast quantity of atoms in the universe, nearly infinite in number. Perhaps these atoms or their precursors were nearly infinitely small at this point of time.

What you don't seem to realize is that "nearly infinite" is a meaningless term. Something is either infinite or finite. Nearly infinite would be finite. Same goes for "nearly infinitely small".

During the period of inflation presumably these atoms (points) somehow moved apart to form 3 dimensional space, they moved from nearly infinitely small to just small.

This “small” is the qualitative or relative aspect (line segment), the size (quality) of which is clearly finite as opposed to nearly or wholly infinite.

Without this relative finite small space between and defining the size of these atoms they could not have emerged from that nearly infinite point.

Try to stick to the topic please. And no, even if doron tries really hard, the topic is not gibberish.

 

[laca]

Thanks

I was using an example to illustrate that I understood the argument.

No, you demonstrated your understanding of the argument. It's not the same as actually understanding the argument.

ETA: just like zooterkin pointed out.

There is little more I can say regarding the argument itself.

FTFY.

 

[doronshadmi]

I'll take that as a "no".

Indeed this is the best you can get by using your weak reasoning.

 

[sympathic]

Indeed this is the best you can get by using your weak reasoning.

Says he who has demonstrated nothing but ignorance, arrogance, and stubbornness.

 

[doronshadmi]

Says he who has demonstrated nothing but ignorance, arrogance, and stubbornness.

sympathic attacs only the person without also deal with the considered subject in http://www.internationalskeptics.com/forums/showpost.php?p=7059130&postcount=14884 .

Please show us the smallest line segemnt, arrogant sympathic, by using your agreed reasoning.

 

[epix]

sympathic attacs only the person without also deal with the considered subject in http://www.internationalskeptics.com/forums/showpost.php?p=7059130&postcount=14884 .

Don't complain. The fringes of atheism manifest themselves that way, if you happen not to notice.

Your link puts you well outside Math city limits:

A point is exactly the smallest possible element.

If the point is the smallest element possible, then it has a magnitude, therefore its size can be compared with other objects. But such a definition has never appeared even in the most esoteric fields of mathematics. The point is treated by all as a dimensionless object -- the point is defined as a particular location within various geometric objects. According to your definition, the length (size) of a line segment minus the size of the points on it equals the actual length of the line segment. That notion calls for a particular computational demonstration, such as

Line is drawn by intersecting two points a and b thus creating line segment a,b. Additional number of points n is drawn on the line segment. So if the initial length of the line segment was L=|a-b| what is the combined length of those line segment separated by the new points after n points have been drawn on it? Is now the length of the a,b segment |a-b| + s*n, where s is the size of the point?

 

[sympathic]

sympathic attacs only the person without also deal with the considered subject in http://www.internationalskeptics.com/forums/showpost.php?p=7059130&postcount=14884 .

Please show us the smallest line segemnt, arrogant sympathic, by using your agreed reasoning.

I do not attack. Just observe and comment. For someone who preaches for a non violent approach I would expect a different choice of words. Another indication that your ideas are nonsenstial.

 

[doronshadmi]

I do not attack. Just observe and comment. For someone who preaches for a non violent approach I would expect a different choice of words. Another indication that your ideas are nonsenstial.

In Hebrew "to attack a mathematical problem" means "to deal with it until it is soleved (or not)".

Please show us the smallest line segemnt, arrogant sympathic (I just observe and comment), by using your agreed reasoning.

 

[doronshadmi]

Don't complain. The fringes of atheism manifest themselves that way, if you happen not to notice.

Your link puts you well outside Math city limits:



If the point is the smallest element possible, then it has a magnitude, therefore its size can be compared with other objects. But such a definition has never appeared even in the most esoteric fields of mathematics. The point is treated by all as a dimensionless object -- the point is defined as a particular location within various geometric objects. According to your definition, the length (size) of a line segment minus the size of the points on it equals the actual length of the line segment. That notion calls for a particular computational demonstration, such as

Line is drawn by intersecting two points a and b thus creating line segment a,b. Additional number of points n is drawn on the line segment. So if the initial length of the line segment was L=|a-b| what is the combined length of those line segment separated by the new points after n points have been drawn on it? Is now the length of the a,b segment |a-b| + s*n, where s is the size of the point?

Please look at:

http://www.internationalskeptics.com/forums/showpost.php?p=7055090&postcount=14852

http://www.internationalskeptics.com/forums/showpost.php?p=7055191&postcount=14855

 

[laca]

In Hebrew "to attack a mathematical problem" means "to deal with it until it is soleved (or not)".

Please show us the smallest line segemnt, arrogant sympathic (I just observe and comment), by using your agreed reasoning.

I can't show you the smallest line segment, because it does not exist, which proves that a line is completely covered by points. How about I show you the dumbest a human can get?