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Cont: Deeper than primes - Continuation 2

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(There is no infinite position) AND (There are infinitely many such positions) is logical contradiction.

(By the way, 3.141592653589793238462643383279502884097169399375 105820974944592307816406286...10 does not represent pi because I have changed one of the digits).
 
Nonpareil said:
Please do some basic research on infinity before trying to make it a centerpiece of your argument.
Click to expand...
This link repeats on the same traditional artificial restriction about the possible place value positions of a given number, whether its defined at the left or right sides of the redix point.

Because of this traditional artificial restriction one simply can't develop mathematical notions as seen, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=11242445&postcount=1036 or http://www.internationalskeptics.com/forums/showpost.php?p=11245518&postcount=1061.

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Once again, if one reads (by not being restricted only to the traditional notions of the considered subjects) this thread from post http://www.internationalskeptics.com/forums/showpost.php?p=11242445&postcount=1036 forward, one can easily realizes that, for example, the following numbers
Code: 
1,000,000,000,...
  100,000,000,...
   10,000,000,...
are not the same, and they are also define their own place values positions, exactly as done among finite numbers.
 
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doronshadmi said:
This link repeats on the same traditional artificial restriction about the possible place value positions of a given number, whether its defined at the left or right sides of the redix point.

Because of this traditional artificial restriction one simply can't develop mathematical notions as seen, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=11242445&postcount=1036 or http://www.internationalskeptics.com/forums/showpost.php?p=11245518&postcount=1061.
Click to expand...

That would be because those "mathematical notions" are wrong, doron.
 
doronshadmi said:
If you read this thread from post http://www.internationalskeptics.com/forums/showpost.php?p=11242445&postcount=1036 you will realize that the following numbers
Code: 
1,000,000,000,...
  100,000,000,...
   10,000,000,...
are not the same.
Click to expand...

Well, you yourself said that all three are 1s with infinitely many 0s. If that doesn't make them the same, how are they different?

Here's another one:
1,000,000,...
Is it one of your three or a different one? How do you tell?
 
Nonpareil said:
That would be because those "mathematical notions" are wrong, doron.
Click to expand...
If they are considered by using only the traditional mathematical notions, then yes, they are understood as wrong.

But this is the main point, one can't value these notions by using only the traditional mathematical notions on this subject.

EDIT:

Here is some concrete example:

1,000,000,... can be considered as a number that is greater than any natural number, such that number h of non-standard analysis has the value 1/1,000,000,000,... < any value of the form 1/n
 
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MetalPig said:
Well, you yourself said that all three are 1s with infinitely many 0s. If that doesn't make them the same, how are they different?

Here's another one:
1,000,000,...
Is it one of your three or a different one? How do you tell?
Click to expand...
In order to show difference, at least two things have to be compared.

If you look at the left side of, for example, these two numbers

Code: 
1,000,000,000,...
  100,000,000,...

you realize that they are not the same number.
 
MetalPig said:
Yes, please do so.

Is my 1,000,000,000,... different from your 1,000,000,000,...?
And how can you tell?
Click to expand...

If there is a difference, it is valued only at the left side of the comparison, for example:
Code: 
1,000,000,000,...
   1,000,000,000,...
 
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MetalPig said:
Are you saying the value of a number depends on the number of spaces in front of it?
Click to expand...
In the case of the numbers at the left side of the redix point, the answer is Yes about the examples that I used.

If, for example, the number of positions is the same, as follows:
Code: 
1,000,000,000,...
1,000,000,000,...
than this is the same number, unless I add, for example 1 to one of them, and in this case we get the inequality
1+1,000,000,000,... > 1,000,000,000,... by 1, even if both of them have the same number of place value positions to the left.
 
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doronshadmi said:
In the case of the numbers at the left side of the redix point, the answer is Yes about the examples that I used.
Click to expand...
All of them have a 1 and infinitely many 0s left of the radix point, so there is no meaningful way of telling if my 1,000,... is bigger or smaller than your 1,000,...
Putting a space in front of the number doesn't usually change the value. If it does in your numbers system, your system is silly.
 
doronshadmi said:
If they are considered by using only the traditional mathematical notions, then yes, they are understood as wrong.
Click to expand...

That would be because they are wrong, doron. You are not very good at math. Trying to invent a new type of mathematics in order to get around this will not change that fact, since your new system - being created, you see, by someone who is not very good at math - is entirely incoherent.

doronshadmi said:
1,000,000,... can be considered as a number that is greater than any natural number, such that number h of non-standard analysis has the value 1/1,000,000,000,... < any value of the form 1/n
Click to expand...

And what number would that be, then?

A hint: infinity is not a number.

doronshadmi said:
In order to show difference, at least two things have to be compared.

If you look at the left side of, for example, these two numbers

Code: 
1,000,000,000,...
  100,000,000,...

you realize that they are not the same number.
Click to expand...

Yes, they are. By definition. They are both a one followed by infinitely many zeroes.

You really ought to read up on how infinity works.
 
Nonpareil said:
A hint: infinity is not a number.
Click to expand...
A number of the form 1,000,000,000,... is not the concept of infinity (notated as ∞) exactly as the traditional first transfinite number aleph0 is not the concept of infinity.

But unlike aleph0, a number of the form 1,000,000,000... can be considered as a number that is greater than any natural number, such that number h of non-standard analysis has the value 1/1,000,000,000,... < any value of the form 1/n

MetalPig said:
If it does in your numbers system, your system is silly.
Click to expand...
Such number system simply do not not satisfy the Archimedean property.
 
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doronshadmi said:
A number of the form 1,000,000,000,... is not the concept of infinity (notated as ∞) exactly as the traditional first transfinite number aleph0 is not the concept of infinity.

But unlike aleph0, a number of the form 1,000,000,000... can be considered as a number that is greater than any natural number, such that number h of non-standard analysis has the value 1/1,000,000,000,... < any value of the form 1/n
Click to expand...

I'm sorry. I thought you were arguing that your worthless non-notation was a means of expressing Aleph-0 as an infinite string of digits.

Oh, no, wait. You were claiming that it replaces Aleph-0 as a means of expressing the cardinality of infinite sets, because its nonsensical behavior could help us get a better understanding of the size of infinite sets or some such nonsense.

Do you even know what you are arguing for at this point?

doronshadmi said:
It has to be stressed that (There is no infinite position) AND (There are infinitely many such positions) - as said in http://www.internationalskeptics.com/forums/showpost.php?p=11246979&postcount=1080 - is a logical contradiction, simply because we are talking about the same object that has infinitely many positions at the right side of the redix point (as seen, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=11246733&postcount=1075).
Click to expand...

No, it's not. The notion of "countably infinite" has already been pointed out to you. Even in a number with infinitely many digits, there is no "infinite position". Every position that exists has a finite place value.

This will not change, no matter how many times you try to say it should.
 
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