God And Infinity, Worlds Without Number Are Numbered To God?

[Rob Osborn]

I propose a slightly better numbering system Rob since your pattern will never get numbers between 0.0 and 0.1. It is as follows:

.0

.1

.2

.3

.4

.5

.6

.7

.8

.9

.01

.11

.21

.31

.41

.51

.61

.71

.81

.91

.02

.12

.22

etc.

Note that there are no repeats. Also note that it reaches .01 which your list never will reach. That said, even this list never reaches 1/3 although it gets arbitrarily close. Even you admit that, "Numbers like that of 1/3 can't be perfectly expressed in this format- .33333333333... " Actually, that's not entirely true. You can express 1/3 in that format as a limit of a sequence. However the sequence itself would not contain 1/3.

I did leave out the .01 but you still get the drift- the principle of where I am coming from. That being- for every column to the right of the decimal placement every possibility will be represented in my list going on into infinity. So aknowledging that for every new column if you were to make a subset of each possibility within each column nad you had to go through each possibility within each subset in that range, you couldn't possibly make a new number no matter what. It just shows that when you look at it slightly different but more within the principles of mathematical logic, it is thus incorrect to make the statement as did Cantor concerning real numbers being larger that the natural numbers. It is easily proven wrong as I have shown.

[asbestosman]

Rob, you've contradicted yourself. On the one hand you talk about 0.33333... never reaching 1/3, but on the other hand you claim that it appears on your list. There's really nothing else for us to discuss regarding Cantor until you comprehend that error.

[The Nehor]

Rob, you've contradicted yourself. On the one hand you talk about 0.33333... never reaching 1/3, but on the other hand you claim that it appears on your list. There's really nothing else for us to discuss regarding Cantor until you comprehend that error.

Just switch to a base 9 system and:

0.3

Done.

[Rob Osborn]

Rob, you've contradicted yourself. On the one hand you talk about 0.33333... never reaching 1/3, but on the other hand you claim that it appears on your list. There's really nothing else for us to discuss regarding Cantor until you comprehend that error.

I haven't contradicted myself. There is no error. Every possible sequence of the numbering system for each column and row is already in my list. The expansion of 1/3 into the decimal system would be .3333333... which is already in my list. Of course it is imperfect in this form and always will be. But I can assure you that every possible number is already in my list and there can be no new ones formed- ever.

[thesometimesaint]

StarGazer:

Eventually the universe will run down, but now and for the forseeable future we are excellerating in our expansion. No one knows why, but the scientists studying it say it is dark energy and they don't know what that is.

[Tarski]

I don't think one has to use the exact language of "math" in order to be understood. Tarski knew what I was talking about. As for Cantor, he, in my opinion, is best known for his diagonal argument- his proof that the real numbers are larger in cardinality than whole numbers. His proof seemingly shows that one can make a list of real numbers of infinite length and he can, from that list make a new number not already in the list. But, I can show how this is a false theory and that he couldn't really do this.

For instance- Let's put some principle in place first. when making a list of numbers, one must include all possibilities for every column- all numbers between 0-9 in sequential rows. Next we must also include that for every shift in column we would also have every possible combination. So, for the next shift it would include every possibility between 0-99. The next colum would be thus- 0-999 and so on forever. Now when we look at this list in this manner knowing that for every possible column (because they can be countable and do truly go on without end), there is already every possibility, no new number could be written from the list because we would already recognize that there are no new possibilities for each new column.

Your rule is not clearly specified. But it doesn't matter since for any list at all one only need look at the diagonal and change each digit by one and the resulting number will disagree with everything in at least one way. For example, the number will disagree with the 100th digit occurring in the 100th row. This can be done with any list!

Done!

Cantor's list does not follow this principle even though it certainly must be in place.

I dare you to read the following slowly--all of it.

Cantor doesn't propose a method for generating a list!!! Read that last sentence again pleeeeez.

Cantor doesn't have a special method for generating a list!!!

Cantor doesn't need a method for generating a list!!!

Cantor doesn't follow a principle for generating a list ....because....... he doesn't generate a list.

He shows why any list fails. It doesn't in the least matter how a list is constructed since it fails simply by virtue of being a list since every list HAS A DIAGONAL which can be trivially altered (add 1 mod 10 to each entry).

Most important sentence: He shows why any list fails. Any list undermines itself.

Don't forget that every column of digits is infinite even if it is all zeros after a certain point. .32 = .32000000000000...............

Never lose sight of that!

Cantor shows that for ANY list of columns, a simple modification of the diagonal will be a list of digits different from any column. No matter what list one uses.

Since you think Cantor proposed a method for generating a list when he didn't, this proves that you never understood Cantor in the first place.

He handles any and all possible lists in one brilliant stroke. Get it? No you don't do you. *sigh*

Every and any list immediately spawns something not on the list. Every list, even your list ( if you could ever make your method of listing clear).

Every list is handled. Why? Because every list has a diagonal. The diagonal can then be altered trivially to produce something not in that list of columns--something that disagrees with the n-th digit in the n-th row for all n.

Every list produces its OWN customized failure--immediately.

Below we see just one list failing but they all fail in the analogous way for the same reason:

The bottom number is nowhere in the list since it is different from the first one in the first place, second one in the second place, third one in the third place and so on forever.

Is there anyone one else on this board (or on the planet) that doesn't get the point? It may have been genius to think of this point, but once it is spelled out, it is obvious!

Pray for a light bulb to go on over your head.

Edited January 25, 2012 by Tarski

[Zeta-Flux]

Rob,

Not to pile on, but I think I understand your method of listing numbers, and I can guarantee that Pi does not occur anywhere on your list. It doesn't occur in the first 20 numbers, and won't ever occur. If you don't believe me, just try the next two numbers, or the next 2000.

[Mudcat]

Hi Rob,

In general at your OP and I suppose at large across the breadth of posts, so far. LDS as a whole seem to grasp this notion of infinite in a much different frame than other Christ believers.

If the premise is true that God the Father, at some point in an infinite timeline was not God the Father but rather began his mortal existence on a world he did not create. And he later became the God that LDS would recognize him as. Then at the very least we would have to acknowledge that "worlds without number" means "worlds without number" - 1.

Respectfully,

Mudcat

[thesometimesaint]

Mudcat:

See

1 Corinthians 8:5

But besides our God was/is/will always be our God. We will always be his servants. Even as joint heirs with Christ.

Also keep in mind that most of the rest of Christian world doesn't accept the Pre-Existence. Where we were all with God eternally.

[Mudcat]

Mudcat:

See

1 Corinthians 8:5

But besides our God was/is/will always be our God. We will always be his servants. Even as joint heirs with Christ.

Also keep in mind that most of the rest of Christian world doesn't accept the Pre-Existence. Where we were all with God eternally.

Hi TSS,.

Don't feel the need to debate Paul's view on monotheism.

Doesn't resolve the issue either. What is the actual fix for it?

[Rob Osborn]

Tarski,

The problem with Cantor's diagonal argument is that he is just playing a simple game of always keeping ahead of the possibilities. In the first number, say we are using numbers 0-9 he can choose one that is different. Out of the nine possibilities he can choose any one of them, for his next number it happens all over again only it gains the power of ten each time. This isn't a proper proof. Think of it this way- It is not hard to imagine that a list could be made that has every possibility in it for every column and row. It is easy to see in this ordered system how no number could possibly ever be left out.Suppose for a moment that we changed the rules around so it was fair. Suppose that we made a subset of numbers of each power of ten with all of it;s possibilities and that one would have to go through each number in that subset before making the new number. Following this method, it clearly shows that in the list, every possibility is accounted for before a new number can be generated. So, thus- no new number sequence can be generated because it is already in the list.

There are a myriad of problems with Cantor's argument. Besides it being a simple math trick, no infinite number is ever counted. Also, only a finite sequence is ever known and anyone who has any sense would know that any finite sequence would already be accounted for in a list showing every possibility. Besides all of that, Cantor's argument says nothing about how the natural numbers compare with the real numbers. Let's say that I was to beat one time on the drum for every real number found. Now in this make believe world lest's say it was possible that we were really able to go through every possible number in the list and for each number we beat once on the drum and we had some poor idiot marking each beat of the drum down on paper acting as a scribe of sorts. Now let;s also say that we beat the drum for each time that Cantor makes a new mark for his argument in his making of his new number. The reality of this is that the beating of the drum would actually represent the natural numbers as the scribe could literally keep making a new mark each time and he could just keep adding one more to his total each time. Now, in this make believe world, in order for Cantor to be right, the guy hitting the drum would have to run out of beats on his drum but of course we know that would be impossible because we know that one more beat could always be beat on the drum for each new number. This circus act would thus continue on forever not only counting all the real numbers, but also the natural numbers and the new number Cantor is making that supposedly isn't in the list. There is a basic principle here if anyone cares to take note-

Any numbering system that is endless or infinite, be it the natural, real or whatever, is like unto the guy beating on the drum and never stopping. If measurement or "cardinality" is the amount of total beats in "completeness" then the cardinality cannot be known because it lacks just that- completeness. Something infinite has no bounds- no actual totality in size or cardinal value. Measurement of an infinite system is not only futile- its complete ridiculousness. The drum will never stop beating for any numbering system of infinity. One drum doesn't continue to beat while the other stops in two infinite numbering systems. That would be a contradiction wouldn't it? If one were to stop and the other were to continue, then we could state the obvious that the one stopped isn't really infinite after all because it would certainly have a finite amount of beats or numbers.

I find it interesting that when one gets away from the abstract of clever little math magic and place the theory in a real world application it becomes quite laughable really.

Besides all of that, you can mirror the real numbers with natural numbers and make the same diagonal argument work to the left of the decimal point so what really is the point?

Edited January 26, 2012 by Rob Osborn

[Rob Osborn]

Rob,

Not to pile on, but I think I understand your method of listing numbers, and I can guarantee that Pi does not occur anywhere on your list. It doesn't occur in the first 20 numbers, and won't ever occur. If you don't believe me, just try the next two numbers, or the next 2000.

But, we are only looking at the real numbers between 0-1 so what then is is it you are asking?

[Rob Osborn]

Here is that mirror-

...123456 - .654321...

...456789 - .987654...

...012345 - .543210...

...789123 - .321987...

...654321 - .123456...

If I were to add one new number on each one (5 turns into 6, etc) I could make my new numbers-

...60497 - .79406...

(note- in the list of my natural numbers, they are made to represent infinitly long numbers that just end in that sequence whereas the real numbers listed are also of infinite length and begin in that sequence. Yeah, I can really do that- we are in make believe land)

Edited January 26, 2012 by Rob Osborn

[Stargazer]

StarGazer:

Eventually the universe will run down, but now and for the forseeable future we are excellerating in our expansion. No one knows why, but the scientists studying it say it is dark energy and they don't know what that is.

What's with the "but"? Expansion acceleration and the heat death of the Universe are not related to each other. Unless somehow dark matter affects energy distribution so as to do something about the rate of entropy increase? I don't think I've heard anything being theorized about this; perhaps you have, and if so, please share.

Edited January 26, 2012 by Stargazer

[asbestosman]

But, we are only looking at the real numbers between 0-1 so what then is is it you are asking?

Zeta probably meant pi - 3 or 1/pi. Those aren't in your list either.

[asbestosman]

Rob is right. You can't count to infinity one drum beat at a time. Sadly, that doesn't disprove Cantor. We do not generate infinite sets that way.

The mirror trick doesn't work because the sequence diverges when there are an endless sequence of non-zero digits for the representation. Also, you seem to be confusing the number with its representation (in decimal notation here). There are many other ways to represent numbers like Roman numerals or solutions to a Diophantine equation.

[thesometimesaint]

Stargazer:

I think the final disallusion of this universe will be a lot further off that we generally like to think about. After all 100 trillion trillion trillion years is a pretty long time from my mortal perspective.

[Rob Osborn]

Rob is right. You can't count to infinity one drum beat at a time. Sadly, that doesn't disprove Cantor. We do not generate infinite sets that way.

The mirror trick doesn't work because the sequence diverges when there are an endless sequence of non-zero digits for the representation. Also, you seem to be confusing the number with its representation (in decimal notation here). There are many other ways to represent numbers like Roman numerals or solutions to a Diophantine equation.

And also sadly speaking- Cantor can't go through any list one by one and make a new infinite number in length- we do not generate infinite numbers that way.....oh wait- there is no such thing as an "infinite number". A "number" has to have known properties. Silly me!

Yeah, I could just make a mark- a line for every number but who cares? It all comes down to "counting" anyway. And who is able to count something that is countless anyway?

[Rob Osborn]

Zeta probably meant pi - 3 or 1/pi. Those aren't in your list either.

My list would contain every possible number between 0-1. Don't think so? Come up with just one number- any number, and we will see if it is listed somehwere in my list. I can assure you that if it is inbetween 0-1 it will certainly be in my list.

Edited January 26, 2012 by Rob Osborn

[lachrymolotov]

There is an amazonian tribe that has no words for different numbers. Imagine what the cultural implications are of something like that. Imagine how that would affect your view of numbers.

Now, imagine you are writing the Bible, thousands of years ago, and your culture has no words or no way to describe the actual amount. How would you express that thought in your words?

To solve this riddle, you only need a simple explanation.

Do you have a name for this number?

999,999,999,959,999,999,999,999,999,999,446,666,666,666,322,222,222,222,222,111,111,111,111,118,888,888,888,888,777,777,775,546,221,654,685,135,468,435,165,153,816,354,684.256789

The truth is, conceptually, it might as well be infinite to anyone. At the very least, you aren't going to be able to describe this number from memory very well. Our minds aren't really set up to deal with crazy numbers, so we develop abstract methods to describe them.

Is it possible that it shouldn't be taken so literally? After all, there are... like... a gazillion stars, anyways, and six times as many worlds.

[Tarski]

My list would contain every possible number between 0-1. Don't think so? Come up with just one number- any number, and we will see if it is listed somehwere in my list. I can assure you that if it is inbetween 0-1 it will certainly be in my list.

Here is the number not in your list.

Take the diagonal of your list and then add one to each digit with the exceptional rule 9 is replaced by 0.

Do this rule all at once. Now. I am not doing something that is taking time. It is done!

Now that is a definite number.

That can't be on your list.

If it were on your list then it would have to be in some position. It would have to be the n-th one in the list for some n.

But then it would disagree in the n-th place so it can't be after all.

It can't be the first one because it is different from that one in the first position.

It can't be the second one because it is different from the second one in the second position.

It can't be the third one because it is different from the third one in the third position.

It can't be the fourth one because it is different from the forth one in the fourth position.

and so on

This works with any list Rob! Not just yours.

In fact, clearly it can be any of them at all because it will disagree in at least that one position with the very one in the list corresponding to that position in the same way as we saw for the first few.

I am not doing something that is taking time. It is done! I am just observing what we have. Namely a number not on your list.

Of course, you have had this explained to you over and over and over so I am sure you still don't get it.

By the way Rob, if God has existed forever and he hasn't created an infinite number of worlds, then he has been wasting a lot of time--an infinite amount of wasted time in fact.

If, as in Mormonism, there were always some God or another all the way back forever into the past, then we have a worse problem. Most of those God would have created no worlds at all.

Edited January 26, 2012 by Tarski

[thesometimesaint]

Tarski:

"By the way Rob, if God has existed forever and he hasn't created an infinite number of worlds, then he has been wasting a lot of time--an infinite amount of wasted time in fact.

If, as in Mormonism, there were always some God or another all the way back forever into the past, then we have a worse problem. Most of those God would have created no worlds at all."

I don't believe it is infinite in the absolute sense of the word. But whatever that number is it is a very large number.

That is a non sequitur. There are about 307 million residents of the US. Not all of them are Presidents of the US.

Edited January 26, 2012 by thesometimesaint

[Tarski]

Tarski,

The problem with Cantor's diagonal argument is that he is just playing a simple game of always keeping ahead of the possibilities. In the first number, say we are using numbers 0-9 he can choose one that is different. Out of the nine possibilities he can choose any one of them, for his next number it happens all over again only it gains the power of ten each time.

No. He has a rule that changes them all at once. Add 1 mod 10.

He is not racing against anything.

Think of it this way- It is not hard to imagine that a list could be made that has every possibility in it for every column and row.

Really. Each row would be infinite and many would have no repeating pattern. How are you, a person who doesn't believe in the infinite imagine so "easily" and infinite list of column where each column is infinitely long?

In fact, there is no such list of all possibilies no matter what you think you can imagine.

It is easy to see in this ordered system how no number could possibly ever be left out.

It is not easy to see. It is false.

. Following this method, it clearly shows that in the list, every possibility is accounted for before a new number can be generated.

That would onlt be true if we only had to deal with finite rows. But we have to deal with numbers like pi (not just approximations but pi itself). There are an infinite number if such.

There are a myriad of problems with Cantor's argument. Besides it being a simple math trick, no infinite number is ever counted.

and the grains of sand on the beach are never counted but they are there. LOL

It isn't a matter of counting in your drum beat sense.

Also, only a finite sequence is ever known and anyone who has any sense would know that any finite sequence would already be accounted for in a list showing every possibility.

But real numbers are given by infinite lists of digits.

I care about what exists in the abstract, not what can be known in your "can-I-count-it-out-loud-before-I-die-sense".

Besides all of that, Cantor's argument says nothing about how the natural numbers compare with the real numbers. Let's say that I was to beat one time on the drum for every real number found. Now in this make believe world lest's say it was possible that we were really able to go through every possible number in the list and for each number we beat once on the drum and we had some poor idiot marking each beat of the drum down on paper acting as a scribe of sorts. Now let;s also say that we beat the drum for each time that Cantor makes a new mark for his argument in his making of his new number. The reality of this is that the beating of the drum would actually represent the natural numbers as the scribe could literally keep making a new mark each time and he could just keep adding one more to his total each time. Now, in this make believe world, in order for Cantor to be right, the guy hitting the drum would have to run out of beats on his drum but of course we know that would be impossible because we know that one more beat could always be beat on the drum for each new number.

What?? This is totally confused. After five beats the number written down by the drummer would be 5. But the diagonal isn't what is in the fifth row. There can't be two things that are fifth in the list. That would ruin what it means to have listed everything.

Besides, the diagonal is infnite in length and so the generated number would be also. The drum would never get to write anything down for THAT real number.

This circus act would thus continue on forever not only counting all the real numbers, but also the natural numbers and the new number Cantor is making that supposedly isn't in the list. There is a basic principle here if anyone cares to take note

Any numbering system that is endless or infinite, be it the natural, real or whatever, is like unto the guy beating on the drum and never stopping. If measurement or "cardinality" is the amount of total beats in "completeness" then the cardinality cannot be known because it lacks just that- completeness. Something infinite has no bounds- no actual totality in size or cardinal value. Measurement of an infinite system is not only futile- its complete ridiculousness. The drum will never stop beating for any numbering system of infinity. One drum doesn't continue to beat while the other stops in two infinite numbering systems.

In the case of countable sets like the natural numbers or the rational numbers, we can do it by a fixed method so that any specific number will eventually be counted.

In the case of the real numbers, there is no method that has that property (that any specific real number would eventually be reached by a single counting method)..

That is the difference.

Countable and uncountable in that technical sense.

[asbestosman]

Rob's argument is not much different than arguing that Russel's barber must shave himself since he shaves everyone while ignoring the second condition--that he only shaves those who do not shave themselves.

Edited January 26, 2012 by asbestosman

[mfbukowski]

Is it possible that it shouldn't be taken so literally? After all, there are... like... a gazillion stars, anyways, and six times as many worlds.

Please don't confuse them with somethng that makes sense.

They are on a roll ("role" applies too.... everyone has an axe to grind.... and we have seen this movie many times before)