Continuum

What is the basis for reason? And mathematics?

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Eodnhoj7
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Re: Continuum

Post by Eodnhoj7 »

wtf wrote: Tue Aug 18, 2020 2:10 am
Eodnhoj7 wrote: Mon Aug 17, 2020 11:50 pm To identify each point as a number is to equivocate 0 to 1 given the point is absent of any qualities.
If you prefer, each point is identical and we associate it with the number that is the location of the point. So there is a point at 2, and a point at pi, and a point at 47, and so forth. You are correct that this is a more precise locution.
A:

To say each point is identical is to say 0=0.

To say 0=0 is to say x=x in that something exists through identity properties.

To say x=x is to say 1=1.

0=1 through x.





B:

To say that a point has a location is to say the point is an entity and as an entity exists as beyond 0 given that zero is nothing. It may be more accurate to say that the point is the position of change from one line (segment) into another line (segment) given the line(s) (segment(s)) are phenomena which are quantifiable given they are forms.

Numbers are the lines not points, unless we equivocate 0 to 1 (which I have no problem with), given the lines are the beginning of form through the projection of nothingness into form. This projection, that of direction, is the beginning of quantifiable forms given that which exists exists through change with this change being the movement of a phenomenon which occurs through direction. One phenomena changes to another, this is movement, and this movement is grounded in direction largely due to the progression from one form into another.
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bahman
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Re: Continuum

Post by bahman »

wtf wrote: Mon Aug 17, 2020 5:24 am
bahman wrote: Mon Aug 17, 2020 3:45 am I should have said that consider that a line exists and is made of points.
Euclid said that 2300 years ago; and contemporary mathematics regards the real line as made of points, each point identified by a real number. So we know this.
bahman wrote: Mon Aug 17, 2020 3:45 am Li according to matematician exists. They call it absoulte instead of infinity.
Absolute what? What are you referring to? There is no largest natural number.

You have a reference to the notation Li? I"m not familiar with it.

There are of course transfinite ordinals and cardinals that go beyond the natural numbers. The smallest transfinite ordinal is called ω, Greek lower case omega. But I don't think you're referring to transfinite ordinals. What exactly are you referring to?
By Li I mean the biggest number, bigger than all trinsfinte. There is no number bigger than this. This number exists according to Cantor.
Skepdick
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Re: Continuum

Post by Skepdick »

bahman wrote: Tue Aug 18, 2020 9:37 am By Li I mean the biggest number, bigger than all trinsfinte. There is no number bigger than this. This number exists according to Cantor.
Perhaps you are referring to Omega (Ω) ?

https://en.wikipedia.org/wiki/Absolute_Infinite
Skepdick
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Re: Continuum

Post by Skepdick »

Eodnhoj7 wrote: Tue Aug 18, 2020 2:22 am To say that a point has a location is to say the point is an entity and as an entity exists as beyond 0 given that zero is nothing.
It depends on what you mean by "exists".

0 is not nothing. It's a point. The symbol "0" merely designates its uniqueness. Like your ID number designates yours.
wtf
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Re: Continuum

Post by wtf »

bahman wrote: Tue Aug 18, 2020 9:37 am By Li I mean the biggest number, bigger than all trinsfinte. There is no number bigger than this. This number exists according to Cantor.
How does Cantor's idea of the absolute infinite, which he thought was God, bear on the discussion of points on a line?
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bahman
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Re: Continuum

Post by bahman »

wtf wrote: Tue Aug 18, 2020 9:51 am
bahman wrote: Tue Aug 18, 2020 9:37 am By Li I mean the biggest number, bigger than all trinsfinte. There is no number bigger than this. This number exists according to Cantor.
How does Cantor's idea of the absolute infinite, which he thought was God, bear on the discussion of points on a line?
The number of points on a line must be bigger than Lambda otherwise we are dealing with a contradiction: Consider a line of length X. Consider that the largest integer number also exist, so-called Lambda. Now we have X/Lambda>0 since if X/Lambda=0 then we could conclude that for any X>Y, X/Lambda=Y/Lambda=0 which means that two different intervals are made of the same number of points. This is absurd. Therefore, X/Lambda>0 which means that there are more points on any line than Lambda, this is contradictory since we assume that there is a larges natural number. Therefore, the largest natural number does not exist.
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bahman
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Re: Continuum

Post by bahman »

Skepdick wrote: Tue Aug 18, 2020 9:44 am
bahman wrote: Tue Aug 18, 2020 9:37 am By Li I mean the biggest number, bigger than all trinsfinte. There is no number bigger than this. This number exists according to Cantor.
Perhaps you are referring to Omega (Ω) ?

https://en.wikipedia.org/wiki/Absolute_Infinite
YES. I was looking for that webpage.
wtf
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Re: Continuum

Post by wtf »

bahman wrote: Tue Aug 18, 2020 10:01 am The number of points on a line must be bigger than Lambda
What is Lambda? Is this what you were earlier calling Li, and what Cantor called Ω?
bahman wrote: Tue Aug 18, 2020 10:01 am otherwise we are dealing with a contradiction: Consider a line of length X. Consider that the largest integer number also exist, so-called Lambda.
No largest integer exists. If Lambda is an integer, so is Lambda + 1. So Lambda can not be the largest integer and there is no largest integer.

But if you think Lambda, whatever it is, is an integer, then it's definitely NOT Cantor's absolute infinite.
bahman wrote: Tue Aug 18, 2020 10:01 am.
Now we have X/Lambda>0 since if X/Lambda=0 then we could conclude that for any X>Y, X/Lambda=Y/Lambda=0 which means that two different intervals are made of the same number of points. This is absurd. Therefore, X/Lambda>0 which means that there are more points on any line than Lambda, this is contradictory since we assume that there is a larges natural number. Therefore, the largest natural number does not exist.
Of course the largest natural number doesn't exist. Everybody knows that.

What on earth are you going on about?

ps -- Just to clarify this point. There is no largest integer. Cantor used the symbol Ω to denote "absolute infinity." But this quantity, which is too big to be regarded as a set or even as a number, is far larger than the mere infinity of the integers. Cantor invented the ordinal numbers, in which you "keep going" after 1, 2, 3, ... to get 1, 2, 3, ... ω, ω+1, ω+2, ..., ω+ω, ω+ω+1, ... ω+ω+ω, ω+ω+ω+ω, ... ω^2, ... ω^3, ..., ω^ω, ... and on and on to get a mind-boggling proper class of ordinal numbers. Cantor thought that the class of all of them was the absolute infinity. So you can see that even if you believe in Cantor's absolute infinity, this quantity, if it's even sensible to call it a quantity, is far far larger than the mere infinity of the integers.

https://en.wikipedia.org/wiki/Ordinal_number
Last edited by wtf on Tue Aug 18, 2020 11:47 pm, edited 1 time in total.
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bahman
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Re: Continuum

Post by bahman »

wtf wrote: Tue Aug 18, 2020 7:19 pm
bahman wrote: Tue Aug 18, 2020 10:01 am The number of points on a line must be bigger than Lambda
What is Lambda? Is this what you were earlier calling Li, and what Cantor called Ω?
bahman wrote: Tue Aug 18, 2020 10:01 am otherwise we are dealing with a contradiction: Consider a line of length X. Consider that the largest integer number also exist, so-called Lambda.
No largest integer exists. If Lambda is an integer, so is Lambda + 1. So Lambda can not be the largest integer and there is no largest integer.

But if you think Lambda, whatever it is, is an integer, then it's definitely NOT Cantor's absolute infinite.
bahman wrote: Tue Aug 18, 2020 10:01 am.
Now we have X/Lambda>0 since if X/Lambda=0 then we could conclude that for any X>Y, X/Lambda=Y/Lambda=0 which means that two different intervals are made of the same number of points. This is absurd. Therefore, X/Lambda>0 which means that there are more points on any line than Lambda, this is contradictory since we assume that there is a larges natural number. Therefore, the largest natural number does not exist.
Of course the largest natural number doesn't exist. Everybody knows that.

What on earth are you going on about?

ps -- Just to clarify this point. There is no largest integer. Cantor used the symbol Ω to denote "absolute infinity." But this quantity, which is too big to be regarded as a set or even as a number, is far larger than the mere infinity of the integers. Cantor invented the ordinal numbers, in which you "keep going" after 1, 2, 3, ... to get 1, 2, 3, ... ω, ω+1, ω+2, ..., ω+ω, ω+ω+1, ... ω+ω+ω, ω+ω+ω+ω, ... ω^2, ... ω^3, ..., ω^ω, ... and on and on to get a mind-boggling proper class of ordinal numbers. Cantor thought that the class of all of them was the absolute infinity. So you can see that even if you believe in Cantor's absolute infinity, this quantity, if it's even sensible to call it a quantity, is far far larger than the mere infinity of the integers.

https://en.wikipedia.org/wiki/Ordinal_number
All I am saying in simple word is that if a line exists, continuum, then it is divisible no matter how many times you try to divide it otherwise you get a point after some divisions, lets call it Ω times, which leads to absurd result.
Skepdick
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Re: Continuum

Post by Skepdick »

bahman wrote: Wed Aug 19, 2020 9:00 am All I am saying in simple word is that if a line exists, continuum, then it is divisible no matter how many times you try to divide it otherwise you get a point.
You are saying the exact opposite thing from your first post. Seems something changed your mind without you noticing?
bahman wrote: Mon Aug 10, 2020 10:49 pm Any continuous thing is divisible to the point.
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bahman
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Re: Continuum

Post by bahman »

Skepdick wrote: Wed Aug 19, 2020 9:10 am
bahman wrote: Wed Aug 19, 2020 9:00 am All I am saying in simple word is that if a line exists, continuum, then it is divisible no matter how many times you try to divide it otherwise you get a point.
You are saying the exact opposite thing from your first post. Seems something changed your mind without you noticing?
bahman wrote: Mon Aug 10, 2020 10:49 pm Any continuous thing is divisible to the point.
You are right. Continuum is not divisible to points. Continuum is made of points.
wtf
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Re: Continuum

Post by wtf »

bahman wrote: Wed Aug 19, 2020 9:00 am All I am saying in simple word is that if a line exists, continuum, then it is divisible no matter how many times you try to divide it otherwise you get a point after some divisions, lets call it Ω times, which leads to absurd result.
You're correct that you can always divide a line segment in half. But you persist in incorrectly using Cantor's absolute infinity Ω. It's not something you can calculate with. It's not a number. It's not a set.
Eodnhoj7
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Re: Continuum

Post by Eodnhoj7 »

Skepdick wrote: Tue Aug 18, 2020 9:47 am
Eodnhoj7 wrote: Tue Aug 18, 2020 2:22 am To say that a point has a location is to say the point is an entity and as an entity exists as beyond 0 given that zero is nothing.
It depends on what you mean by "exists".

0 is not nothing. It's a point. The symbol "0" merely designates its uniqueness. Like your ID number designates yours.
A point is that which is absent of any form or volume, it can only be observed as the change of one phenomenon to another. Phenomenon composed of points are composed of change.

An example of this would be the line. The point observes the change of one line into another line.

Another example would be all phenomenon resulting in points. An object at a distance is reduced to a point. An object up close is reduced to points. The change in one position of a phenomenon to another results in the phenomenon expanding an contracting from a point. The expansion or contraction of a phenomenon is reduced to (a) point(s) where the point is the median of change from one phenomenon to another.
wtf
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Re: Continuum

Post by wtf »

Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am
A point is that which is absent of any form or volume, it can only be observed as the change of one phenomenon to another. Phenomenon composed of points are composed of change.
That's an interesting philosophical point of view.

It is not the contemporary mathematical view, for what it's worth.

I do not know what you mean by a point being observed. There is no observer in mathematics. Rather, what there is, is the real number line. Each location on the line is represented by a real number, which you can think of as the address of that location. Then we can identify any point on the line with the address of the point's location.

For example pi = 3.1415... is a particular real number, and there is a particular point at that location on the real number line. We can call the point pi or we can make a big deal about that point not "really" being pi. The former viewpoint lets us get on with the study of the real numbers, which leads to the study of n-dimensional spaces that the physicists describe the universe with. The latter view just gets you into pointless philosophical arguments but your time would be better spent learning about the real numbers.

The bottom line is that there is no change needed to define a mathematical object. We can define the real numbers, and the number pi, with perfect logical rigor. Having done so, pi is eternal. It will always be that particular number, the point living at that particular address on the real number line. Each point is static and in mathematics, it exists. The set of real numbers, and each and every individual real number, has mathematical existence. Unchanging mathematical existence.

That is my two cents on the subject.
Eodnhoj7
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Re: Continuum

Post by Eodnhoj7 »

wtf wrote: Thu Aug 20, 2020 5:23 am
Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am
A point is that which is absent of any form or volume, it can only be observed as the change of one phenomenon to another. Phenomenon composed of points are composed of change.
That's an interesting philosophical point of view.

It is not the contemporary mathematical view, for what it's worth.

I do not know what you mean by a point being observed. There is no observer in mathematics. Rather, what there is, is the real number line. Each location on the line is represented by a real number, which you can think of as the address of that location. Then we can identify any point on the line with the address of the point's location.

Each number is an act of observation itself given it is a division or multiplication of a phenomenon through the angle of the observer. To divide an orange into x parts necessitates the observr to form the orange in accords to the mode of observation. In simpler terms x is projected onto the orange by the observer and divided as such. The same applies to the number line if not more so given the line is a perpetually finite number approaching infinity, thus is always changing in accords to what number is being observed by the observer.

For example pi = 3.1415... is a particular real number, and there is a particular point at that location on the real number line. We can call the point pi or we can make a big deal about that point not "really" being pi. The former viewpoint lets us get on with the study of the real numbers, which leads to the study of n-dimensional spaces that the physicists describe the universe with. The latter view just gets you into pointless philosophical arguments but your time would be better spent learning about the real numbers.

The bottom line is that there is no change needed to define a mathematical object. We can define the real numbers, and the number pi, with perfect logical rigor. Having done so, pi is eternal. It will always be that particular number, the point living at that particular address on the real number line. Each point is static and in mathematics, it exists. The set of real numbers, and each and every individual real number, has mathematical existence. Unchanging mathematical existence.

"An example of this would be the line. The point observes the change of one line into another line.

Another example would be all phenomenon resulting in points. An object at a distance is reduced to a point. An object up close is reduced to points. The change in one position of a phenomenon to another results in the phenomenon expanding an contracting from a point. The expansion or contraction of a phenomenon is reduced to (a) point(s) where the point is the median of change from one phenomenon to another."

The observation of a phenomenon, linear or not, contracting and expanding from a point necessitates a quantifiable entity contracting or expanding from this very same point. All numbers, as grounded in the quantification of forms, expand and contract from a simple point where the point is the means of change from one quantifiable form into another.

This is best expressed through the line where each point is a position of change from one line into another. This change from one line into another results in the recursion of line where it exists as fractals. Each fractal is both 1/x of the original line, as both a fractal and fraction, and dually is x number of whole lines when each line is viewed individually. The position of points necessitates the one line resulting in further line segments, each being infinite in length considering they are composed of further lines as units. The position of the point observes the line changing into further lines through itself where the line exists through a circular self referentiality that occurs through the 0d point. The 0d point is the line changing into another line with this line circularit self referencing itself through fractions much in the same manner a being manifests in a new variation of itself, yet is still itself, when faced with a complete absence or annihilation of the very same being.

The line as composed of points is the line composed of change where this change is a reflection of the angle of awareness of the observer in selectively seeing a series of finite entities or rather in seeing a different number of finite numbers each time the line is observed. The line is a projection of the number the observer manifests through a selective perception.



That is my two cents on the subject.



All numbers are modes of change given that the equivocate to a variety of phenomenon through which they are counted. For example in counting 1 horse we observe 1 as equivocating to not just a phenomenon that changes through time and space but also 1 as equivocating to a variety of other phenomenon, such as a jet, therefore necessitating 1 as a mode of change.

It equates to a variety of phenomenon thus is always changing, and what it equates to directly goes through a mode of change as well.

Relative to a number such as Pi it is an irrational (or transcendental) number which is perpetually changing thus causing the line to expand or contract given each set of digits observed is a new fraction of the line. Given Pi's infinite regress to fractions (and fractals of the number line) each position is a result of the number being observed. All numbers are the means in which change is observed as a mode of perception.
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