Galileo's paradox

[Moontanman]

test

[QuarkH]

14 hours ago, sluggo said:

I don't accept Cantor's ideas of infinite sets. He declares infinite sets have an independent existence (without proof), and are complete things. By definition they are incomplete without a limit. His idea is a contradiction of terms.

His 1 to 1 correspondence is correct for some things, such as 'there are as many even integers as odd integers'.

D:{1 3 5 7 9 ...}

E:{2 4 6 8 10 ...}

There are no common elements.

We begin with finite sets from N, like {1 2 3 4}. We extend it by adding (n+1).

When does N become infinite?

Cantor claims his idea of 'transfinite' numbers was divine inspiration and he was a messenger. If true, when the paradoxes appeared, who was at fault? If Cantor, was God an accomplice? Could that have been a case for 'defamation of character'?

Statistics vs Cantor one to one.

Number of members within a constant interval of N, 1 thru 100.

Even, 50/100 = .50

Squares, 10/100 = .10

Cubes, 4/100 =.04

Cantor's 1 to 1 correspondence is not compatible with statistics.

It yields 1.00 for the above classes.

Statistics is applied math concepts to a broad range of human activities, used daily around the world.

After years of effort, I have a paper that exposes his errors in the diagonal argument.

Ah well. I am the fool for thinking I was dealing with a rational person.

[sluggo]

On 2/27/2024 at 4:33 AM, QuarkH said:

Ah well. I am the fool for thinking I was dealing with a rational person.

That's the canned answer I get from every forum, when the poster cannot accept the possibility they may be wrong.

It's unlikely they ever tried to disprove Cantor's diagonal argument, and accepted it based on authority figures, science be decree.

 

[Diamonds]

The infinite volume of space can not be descriped by infinite amount of numbers. If every detail, every star, planet and sandgrain should have an unique name using only numbers in naming them there are not enough numbers even in infinity.

That is why we must have letters too from A to Z. I got this idea from the JW bible. 

Infinite amount of numbers are just not enough to describe infinity. 

 

[Diamonds]

There are many points of view why it is impossible. 

If we use unique coordinates describing every point in space this only takes every number there is available. And there are constants that can not change but allways remain the same. For instance speed of light. If it is allowed to use each number only once it is impossible.  

Infinity needs more than infinite amount of numbers. For instance the Letters and the words.

 

 

[OceanBreeze]

Infinity is a mathematical concept . There is no way to quantify infinity whether you use numbers, letters cats and dogs or any other method.

[Halc]

On 8/26/2024 at 5:53 AM, Diamonds said:

If every detail, every star, planet and sandgrain should have an unique name using only numbers in naming them there are not enough numbers even in infinity.

Not so.  A single unique integer is enough to identify any one of those things, and at a specific duration of time.  Thus the list of all things in this universe* has the same cardinality as the set of whole numbers.

* The whole universe, not just the visible part, but the comment presumes counterfactual definiteness, without which distant and little 'things' don't exist by the usual definition of existence.

On 8/26/2024 at 5:53 AM, Diamonds said:

That is why we must have letters too from A to Z

Numbers can encode those letters, so the letters add no additional utility.  In fact, that is one trivial way to describe any 'thing' with just one number.  Describe it in text, and the ascii encoding of that text is the single integer in question. There are more mathematically precise ways to do it, but this method suffices.  The entire JW bible can be (and is often) expressed with a single integer.

On 8/26/2024 at 5:53 AM, Diamonds said:

Infinite amount of numbers are just not enough to describe infinity. 

More than enough, since infinity is described in multiple finite sources, each of which corresponds to a single number. You are apparently asserting random things which you hope are true, but are demonstrably not and thus are not rational.

On 8/26/2024 at 6:03 AM, Diamonds said:

If we use unique coordinates describing every point in space this only takes every number there is available. 

A region of spacetime (a box of a certain size, for a certain duration) requires 8 coordinates (integers), which can be encoded with a single integer similar to the way the rationals (with integer numerator and denominator each) can be enumerated with a single whole number. They're countable. Similarly, and region of spacetime, of any desired precision, can be expressed with a single integer, and is thus countable.

What is impossible is absolute coordinates for any given thing.  An origin must be selected, making the coordinate position of any given region relative to that arbitrarily selected origin.  So the location of Earth cannot be specified without using a relation of some kind, hence it not having an absolute location.

 

On 8/26/2024 at 6:03 AM, Diamonds said:

And there are constants that can not change but allways remain the same. For instance speed of light. If it is allowed to use each number only once it is impossible.  

I have no idea why you think the speed of light is relevant to specification of the location of something, except perhaps in the optional effort to utilize natural units.

Why does the speed of light not have permission to use any given number more than once?  Why would the speed of light need to use a number at all?  It isn't an abstracting entity like we are.  I.E. what did you mean by that assertion?

Edited August 30 by Halc

[OceanBreeze]

 

On 8/26/2024 at 4:53 PM, Diamonds said:

If every detail, every star, planet and sandgrain should have an unique name using only numbers in naming them there are not enough numbers even in infinity.

 

1 hour ago, Halc said:

More than enough, since infinity is described in multiple finite sources, each of which corresponds to a single number. You are apparently asserting random things which you hope are true, but are demonstrably not and thus are not rational.

 

Halc, are you claiming that an infinite number of things is countable?

The only sense in which infinity can be considered countable is if you count with whole numbers, but it would take an infinite amount of time and you still would never be able to count everything.

The acceptable answer is that infinity is not a number; it is a mathematical concept only, and as such it is uncountable.

Sure, you can assign a single symbol to infinity; ∞ and count that with a single digit. Anyone who thinks that is the same as counting to infinity is delusional.

I repeat what I wrote earlier: Infinity is a concept, a useful idea, that is related to numbers and counting systems; but it is not a number and therefore it is not countable.

If a set is countable, with a finite result, it is not an infinite set by definition.

[Halc]

57 minutes ago, OceanBreeze said:

Halc, are you claiming that an infinite number of things is countable?

Yes, i do, by at least two different methods described in my prior post.  Yes, countable with natural numbers (not integers).

58 minutes ago, OceanBreeze said:

it would take an infinite amount of time and you still would never be able to count everything.

It being countable means there is a 1-1 bijection between the whole numbers and each 'thing'.  I can for instance, find one natural number that corresponds to a particular pebble on Pluto.  How much time it takes to determine that number is finite, and entirely besides the point of the claim.

You seem to suggest that it would take unbounded time to do the work of explicitly assigning a number to each thing, which is true, but it is also true of the integers, unless you're suggesting that the integers are not countable.

1 hour ago, OceanBreeze said:

The acceptable answer is that infinity is not a number

Not a natural number, agree.  The OP seems to presume otherwise, and runs into all sorts of contradictions due to that assumption.

The wiki article sort of implies that infinity is a number, but a cardinal number, which can be compared with other cardinal numbers.

I'm not sure about infinity being uncountable. I mean I'm not sure if there is a bijection between the natural numbers and the cardinal numbers since one cannot define adjacent numbers. If one is never sure if there is a cardinality between X and Y, then you can't count to Y.

1 hour ago, OceanBreeze said:

If a set is countable, with a finite result, it is not an infinite set by definition.

You seem to be unfamiliar with the concept of countable infinity vs uncountable infinity. This is what is being referenced when I say that the list of things in the universe falls into the former camp.  A set being countable in no way means that it has a finite number of members, but yes, if it has a finite count, then it is a set with finite members by definition.

[OceanBreeze]

On 8/31/2024 at 12:15 AM, Halc said:

Yes, i do, by at least two different methods described in my prior post.  Yes, countable with natural numbers (not integers).

It being countable means there is a 1-1 bijection between the whole numbers and each 'thing'.  I can for instance, find one natural number that corresponds to a particular pebble on Pluto.  How much time it takes to determine that number is finite, and entirely besides the point of the claim.

You seem to suggest that it would take unbounded time to do the work of explicitly assigning a number to each thing, which is true, but it is also true of the integers, unless you're suggesting that the integers are not countable.

Not a natural number, agree.  The OP seems to presume otherwise, and runs into all sorts of contradictions due to that assumption.

The wiki article sort of implies that infinity is a number, but a cardinal number, which can be compared with other cardinal numbers.

I'm not sure about infinity being uncountable. I mean I'm not sure if there is a bijection between the natural numbers and the cardinal numbers since one cannot define adjacent numbers. If one is never sure if there is a cardinality between X and Y, then you can't count to Y.

You seem to be unfamiliar with the concept of countable infinity vs uncountable infinity. This is what is being referenced when I say that the list of things in the universe falls into the former camp.  A set being countable in no way means that it has a finite number of members, but yes, if it has a finite count, then it is a set with finite members by definition.

Halc, I am not totally unfamiliar with the concept of a countable infinity. I just do not agree with describing an infinity as “countable” simply because a bijection (correlation) can be made between an infinite amount of anything and an infinite set of numbers.

Countable, to my way of thinking, means that a finite result can be reached. The fact that you can make a correlation, but even if you count forever and can never reach a definitive result, proves you cannot count to infinity.

I know I am repeating myself but infinity is not a number; it is a mathematical concept and as such is uncountable. That is not just my opinion; you can find that same description of infinity with a brief search.

But I won’t argue the point any further. I recognize there are different points of view; but I will not agree even if the discussion continues for an infinity.

[sluggo]

What is math?

How to find a dimensionless point, which is also invisible!

One way is the 'blob' method. A small amount of material, (ink, graphite, chalk, etc.) is applied  to the surface of a second material to form an image.

The point is somewhere within the blob. As a coordinate it is assigned to the nearest tangible object such as a molecule. That means the position is not absolute.

This process is extended for lines as the locus of a point, areas, etc.

Thus geometry is a large batch of fudge.

Mathematics makes use of a continuous straight line which can be divided into intervals representing 'real' numbers.

How can a continuous line be divided?

If 0*n=0 for all n, how many points n, are required for an interval to represent a unit?

So much for rigorous definitions.

The only numbers we have are the counting numbers/integers {1, 2, 3, ...} from the set N. The integers represent collections of objects stripped of all properties. Counting is the basic form of measurement, which like time became a necessity for human activity. The extension of numbers in the form of 'real' is a notational convention using place value, i.e. an abstract decimal system. A length of material may be specified to 10 decimal places, but the cuts have to be between molecules!

To say N is 'infinite' means it has no last term, and implies nothing concerning magnitude. The idea that N exists as a complete thing is nonsense.

An arrest warrant does not exist until it is written and authorized. Governmental regulations are drafted and voted into laws. Houses don't exist until built.

Numbers don't exist until they are written, thus infinity is not a property of N, but the ability to repeat the finite Peano method of forming larger integers, as recognized by Poincare and Wittgenstein. I.e. the process of expanding the set N is 'infinite', NOT the set.

-----------------------------------

Cantor quote from Ewald, W., From Kant to Hilbert, Oxford 1996

"One must only understand the expresion "finished" correctly.  I say of a set that it can be thought of as finished (and call such a set, if it contains infinitely many elements, "transfinite" or "suprafinite") if it is possible without contradiction (as can be done with finite sets) to think of all its elements as existing together, and to to think of the set itself as a compounded thing for itself; or (in other words) if it is possible to imagine the set as actually existing with the totality of its elements."

 

Cantor's idea of 'a thing with no end yet complete' is a contradiction of terms.

The word 'infinite' literally means without bounds, but boundaries are required to make measurements!

[sluggo]

Never accepted his idea.

Latest paper refuting 'Cantor Diagonal Argument'

https://drive.google.com/file/d/1AT5rCprz3fB0JqcP9UwE_e_GhaBDeqJP/view?usp=sharing