• Security incident: ISF was recently accessed by intruders. Please change your password, and change it anywhere else you used it. Read more

Cont: Deeper than primes - Continuation 2

Status
Not open for further replies.
Last edited:
doronshadmi said:
By following after the standard definition (as seen in http://www.internationalskeptics.com/forums/showpost.php?p=10617284&postcount=314)
Click to expand...

By following after? The standard definitions are the only ones that matter. Any other meaning you might imagine for, say, limit wouldn't be limit any more. It would be something else. You cannot show Mathematics to be broken simply by changing the meaning of things.

...what is your answer to this question?
Click to expand...

The proof can be found in lots of places. Just about any decent mathematics text covering convergent sequences would consider geometric sequences of the form, AxR1-n. They would provide a more general result than you require.
 
doronshadmi said:
Please provide a link to such place.
Click to expand...

"Text" would, in general, not be something that corresponds to a link. Be that as it may, you seem to like Wikipedia, so let's go with two similar links from there. How about Geometric progressionWP and Geometric seriesWP.
 
jsfisher said:
"Text" would, in general, not be something that corresponds to a link. Be that as it may, you seem to like Wikipedia, so let's go with two similar links from there. How about Geometric progressionWP and Geometric seriesWP.
Click to expand...
I do not see any rigorous proof there, please guide to such proof.
 
doronshadmi said:
jsfisher said:
"Text" would, in general, not be something that corresponds to a link. Be that as it may, you seem to like Wikipedia, so let's go with two similar links from there. How about Geometric progressionWP and Geometric seriesWP.
Click to expand...
I do not see any rigorous proof there, please guide to such proof.
Click to expand...


I'm sorry you are having trouble following these things. Focus on the "Infinite geometric series" section of the first article and the "Proof of convergence" of the second.
 
jsfisher said:
I'm sorry you are having trouble following these things. Focus on the "Infinite geometric series" section of the first article and the "Proof of convergence" of the second.
Click to expand...

∞ does not rigorously define infinity, so since "Infinite geometric series" and "Proof of convergence" use it, they do not define any rigorous proof.

A rigorous proof must be based on infinity as defined by transfinite cardinality for example: aleph0 < aleph1 < aleph2 < ... etc.
 
Last edited:
doronshadmi said:
∞ does not rigorously define infinity, so since "Infinite geometric series" and "Proof of convergence" use it, they do not define any rigorous proof.
Click to expand...


Oh, I see. It is limits you don't understand. Odd that, since that is the very thing you have been trying to attack. Good luck with that. It is usually best to understand what you object to rather than simply object.

I take that back. It is not just limits you don't understand for the matter at hand. Infinite sequences escape your grasp, too. Otherwise, you'd know why your statement quoted here is, as they would say on the old Perry Mason TV series, incompetent, irrelevant, and immaterial.
 
jsfisher said:
I take that back.
Click to expand...

It does not change the fact that a rigorous proof must be based on infinity as defined by transfinite cardinality for example: aleph0 < aleph1 < aleph2 < ... etc.

∞ does not provide the necessary rigorous terms exactly because it does not distinguish between aleph0, aleph1, aleph2, ... etc.
 
Last edited:
doronshadmi said:
It does not change the fact that a rigorous proof must be based on infinity as defined by transfinite cardinality for example: aleph0 < aleph1 < aleph2 < ... etc.

∞ does not provide the necessary rigorous terms.
Click to expand...

As I said, your failure to understand limits and sequences allows you to believe your objection has substance. It does not. Why it does not is basic to both concepts.

However, just so you don't get completely hung up on a pro forma objection, one without substance, perhaps you might consider the question of where would the proof break down if your objection did have substance. Put another way, what purpose does the infinity used in the proof serve, since at no point does infinity itself in any of its possible forms ever actually enter into the argument.
 
doronshadmi said:
No, I improve it by omitting the "|N|+1=|N|" stuff and its wrong related conclusion, which according to it 0.999...10 = 1 without using 0.000...110.

But now I have realized that it can't be done without adding 0.000...110 to 0.999...10
Click to expand...

You do know that 0.9999... is equal to 1.0. In fact, there is no such number as 0.00...1.

Check this out:

x = 0.999...
10x = 9.999...
10x = 9+0.999...
10x = 9 + x
9x = 9
x = 1

In fact we have a wiki page for you. 0.999...WP

It even gives you several examples!!!
 
Little 10 Toes said:
You do know that 0.9999... is equal to 1.0. In fact, there is no such number as 0.00...1.

Check this out:

x = 0.999...
10x = 9.999...
10x = 9+0.999...
10x = 9 + x
9x = 9
x = 1

In fact we have a wiki page for you. 0.999...WP

It even gives you several examples!!!
Click to expand...

I know how he'll respond. He's still got his meaningless notation that solves all his problems. Just wait. Lack of self-consistency won't deter him, either.
 
jsfisher said:
where would the proof break down if your objection did have substance.
Click to expand...
There is no rigorous proof by using inaccurate form like ∞ for infinity.

jsfisher said:
Put another way, what purpose does the infinity used in the proof serve, since at no point does infinity itself in any of its possible forms ever actually enter into the argument.
Click to expand...
Infinity itself (notated by ∞ inaccurate form) actually enters into the argument, exactly as seen in "Infinite geometric series" section of Geometric progressionWP or in "Proof of convergence" section of Geometric seriesWP.
 
Last edited:
doronshadmi said:
There is no rigorous proof by using inaccurate form like ∞ for infinity.
Click to expand...

Good thing, then, the proof uses no form of infinity.

Infinity itself (notated by ∞ inaccurate form) actually enters into the argument, exactly as seen in "Infinite geometric series" section of Geometric progressionWP or in "Proof of convergence" section of Geometric seriesWP.
Click to expand...

The appearance of a particular symbol in a notation does not make "infinity" a part of the proof. Look at the definition for 'limit' as the domain variable tends to "infinity". No where does "infinity" of any form find its way into the definition, and no where does "infinity" of any form find its way into the proof.

If you think otherwise, go ahead and identify exactly where "infinity" enters into the prove (as something other than mere notation for 'limit').
 
Status
Not open for further replies.

Share this page

ISF - Join now!

Every member here is approved by hand. No bots, no spam, just people who care about evidence and honest debate.

Membership is free!

Create your free account

Back
Top Bottom