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Old 30th April 2015, 04:40 AM   #361
doronshadmi
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Originally Posted by jsfisher View Post
[Highlighted text added.]
Great. So now all that is left for you to provide is an actual definition.
What I wrote is much more rigorous than your fantasy of "the series for an infinite sequence [that] is, by definition the limit of the sequence of partial sums".

Your definition is a fantasy (relatively or absolutely) exactly because
Originally Posted by jsfisher View Post
...determining the limit of the sequence of partial sums does not involve infinity at any step.
so your call for definition does not hold water.
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Old 30th April 2015, 04:55 AM   #362
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Originally Posted by doronshadmi View Post
What I wrote is much more rigorous than your fantasy of "the series for an infinite sequence [that] is, by definition the limit of the sequence of partial sums" exactly because your definition, by your own words,
Curious you think the word you inserted belongs there. It is further evidence you don't understand the meaning of 'limit' nor 'sequence'. And, no, you didn't provide anything to discredit what I have written. You merely complained about something that did not even appear in the proof.

Nevertheless, you may use your own doron-limit if you wish. You just need to define it. Why has defining things proven so difficult for you?
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Old 30th April 2015, 04:59 AM   #363
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Originally Posted by Little 10 Toes View Post
define Doron-level please.
There is no doron-level, but only the different levels of place value method, for example:

1 in 0.00110 is in higher level than 9 in 0.000910
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Old 30th April 2015, 05:10 AM   #364
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Originally Posted by jsfisher View Post
Curious you think the word you inserted belongs there. It is further evidence you don't understand the meaning of 'limit' nor 'sequence'.
Please support your argument about me (that I "don't understand the meaning of 'limit' nor 'sequence'" because I'v added the word [that]) in details.

Only if you do that rigorously, then and only then you can start to talk about the validity of your, so called, definition.
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Old 30th April 2015, 05:40 AM   #365
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Originally Posted by doronshadmi View Post
Please support your argument about me (that I "don't understand the meaning of 'limit' nor 'sequence'" because I'v added the word [that]) in details.
Not 'because'. The curious word addition you made was additional evidence. My statement was correct without the addition, and becomes a non-sentence with the addition.

Quote:
Only if you do that rigorously, then and only then you can start to talk about the validity of your, so called, definition.
Validity of a definition? I see you are back to trying to disprove meaning. It doesn't work that way. Definitions stand as is, whether you understand them or like them or would prefer something else.
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Old 30th April 2015, 05:43 AM   #366
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Originally Posted by jsfisher View Post
you didn't provide anything to discredit what I have written.
Since infinity is not involved in your definition of limits, no sum of any given sequence is identical to a given limit, accept in your fantasy.
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Old 30th April 2015, 05:47 AM   #367
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EDIT:

Originally Posted by jsfisher View Post
Validity of a definition?
Exactly, since infinity is not involved in your definition of limits. As a result it is no more than your fantasy, simply because no sum of any given sequence is identical to a given limit if infinity is not involved.

Once again your dogmatic philosophical (and I would even add religious) approach about definitions, is exposed.
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Old 30th April 2015, 05:48 AM   #368
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Originally Posted by doronshadmi View Post
Since infinity is not involved in your definition of limits, no sum of any given sequence is identical to a given limit, accept in your fantasy.
The definition of series makes your statement incorrect. Please stop trying to disprove definitions. They are not subject to that sort of thing.
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Old 30th April 2015, 06:00 AM   #369
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Originally Posted by jsfisher View Post
The definition of series makes your statement incorrect. Please stop trying to disprove definitions. They are not subject to that sort of thing.
Your definition of limits is incorrect exactly because infinity is not involved in it.

Its validity it is no more than your fantasy, exactly because no sum of any given sequence is identical to a given limit if infinity (in its relative or absolute forms) is not involved in the definition.
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Old 30th April 2015, 06:07 AM   #370
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Originally Posted by jsfisher
It is perfectly acceptable for 0 < |an - L|
In that case it is perfectly acceptable that, for example, 0.999...10 < 1
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Old 30th April 2015, 06:24 AM   #371
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Originally Posted by doronshadmi View Post
Your definition of limits is incorrect exactly because infinity is not involved in it.
Still, despite your protestations, the definition stands unphased.

Now, it may be its utility you challenge. Challenge away, but the best way to do what would be to define for us your new and improved version of doron-limit. Who knows what great insight your alternate might provide. You need only define doron-limit so we can proceed to the next step.
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Old 30th April 2015, 06:26 AM   #372
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Originally Posted by doronshadmi View Post
Originally Posted by jsfisher
It is perfectly acceptable for 0 < |an - L|
In that case it is perfectly acceptable that, for example, 0.999...10 < 1
My statement is consistent with the meaning of 'limit'. Your statement is not.
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Old 30th April 2015, 07:04 AM   #373
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Originally Posted by jsfisher View Post
My statement is consistent with the meaning of 'limit'.
Your statement is consistent with the current agreement about the meaning of 'limit', which is wrong exactly because infinity is not involved.

As a result 0 < |an - L| is perfectly acceptable and so is 0.999...10 < 1, simply because they are inseparable of each other.
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Old 30th April 2015, 10:07 AM   #374
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Originally Posted by doronshadmi View Post
Your statement is consistent with the current agreement about the meaning of 'limit'
Current? Well, I suppose. These things don't tend to change, though, especially when they are as useful as this one is.

Quote:
...which is wrong exactly because infinity is not involved.
That doesn't make it wrong. It is one of those things that makes it useful, though.

Quote:
As a result 0 < |an - L| is perfectly acceptable
Not just acceptable. It is entirely consistent with the definition of 'limit'. (That is not to say it cannot be zero, but that 'limit' allows it to be positive.)

Quote:
...and so is 0.999...10 < 1, simply because they are inseparable of each other.
Repeating a bogus statement makes it no less bogus. You'd need to provide, you know, one of those proof things to show how your conclusion follows.

On the other hand, if you'd prefer something besides 'limit' to explore, all you need do is define that something first.
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Old 30th April 2015, 12:58 PM   #375
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Originally Posted by jsfisher View Post
Current? Well, I suppose. These things don't tend to change, though, especially when they are as useful as this one is.
Usefulness in not fixed, it can be developed beyond its current state, for example the usefulness of the difference between 0.999...10 and 1, if infinity is involved in its relative or absolute forms, exactly as explained in http://www.internationalskeptics.com...&postcount=358.


Originally Posted by jsfisher View Post
That doesn't make it wrong. It is one of those things that makes it useful, though.
The current definition is one of those things that is restricted only to finitism.

As a result it can't distinguish, for example, between the sum over (0.910, 0.0910, 0.00910, 0.00110) = 1 and the sum over (0.910, 0.0910, 0.00910, ...) < 1


Originally Posted by jsfisher View Post
Not just acceptable. It is entirely consistent with the definition of 'limit'. (That is not to say it cannot be zero, but that 'limit' allows it to be positive.)
The current definition of limit is inconsistent exactly because 0 < |an - L| and, for example, 0.999...10 < 1 are wrongly defined as separable of each other (and as a result 0 < |an - L| AND 0.999...10 = 1).


Originally Posted by jsfisher View Post
Repeating a bogus statement makes it no less bogus.
It is a perfectly clear and valid statement that gets rid of the separability (as described above) that is at the heart of your currently accepted definition, which is wrong because of this separability.
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Old 30th April 2015, 03:15 PM   #376
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Originally Posted by doronshadmi View Post
Usefulness in not fixed, it can be developed beyond its current state
We all anxiously await your definition of 'doron-limit' to facilitate this great development.

Quote:
...The current definition is one of those things that is restricted only to finitism.
I have no idea what you mean. It handles, for example, infinite series quite well.

Quote:
As a result it can't distinguish, for example, between the sum over (0.910, 0.0910, 0.00910, 0.00110) = 1 and the sum over (0.910, 0.0910, 0.00910, ...) < 1
I find it comforting that Mathematics provides the result, 0.999... = 1.

Quote:
The current definition of limit is inconsistent exactly because 0 < |an - L|
In what way is it inconsistent? You have show no contradiction. Moreover, the greater than 0 is not a requirement of the definition of 'limit'.

Quote:
...and, for example, 0.999...10 < 1 are wrongly defined as separable of each other
No where in Mathematics is 0.999... defined to be less than 1.

Quote:
(and as a result 0 < |an - L| AND 0.999...10 = 1).

It is a perfectly clear and valid statement that gets rid of the separability (as described above) that is at the heart of your currently accepted definition, which is wrong because of this separability.
Your disdain for some definitions in Mathematics is irrelevant.
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Old 30th April 2015, 08:42 PM   #377
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Originally Posted by doronshadmi View Post
There is no doron-level, but only the different levels of place value method, for example:

1 in 0.00110 is in higher level than 9 in 0.000910
Please show someone else's work that mentions "levels" in the place value method.

Edit:

here's more proof for you that 0.999999... = 1.0

Let x=1.0
1/3 x = .33333333...
1/3x + 1/3x = 2/3x = .6666666...
2/3x + 1/3x = x = .999999999999...

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Old 30th April 2015, 11:23 PM   #378
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Originally Posted by Little 10 Toes View Post
Please show someone else's work that mentions "levels" in the place value method.

Edit:

here's more proof for you that 0.999999... = 1.0

Let x=1.0
1/3 x = .33333333...
1/3x + 1/3x = 2/3x = .6666666...
2/3x + 1/3x = x = .999999999999...
0.333... < 1/3 x, so your example does not work.
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Old 30th April 2015, 11:36 PM   #379
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Originally Posted by jsfisher View Post
Your disdain for some definitions in Mathematics is irrelevant.
Your failure to understand the fallacy of 0 < |an - L| AND 0.999...10 = 1, is indeed disdain for Mathematics.


Originally Posted by jsfisher View Post
We all anxiously await your definition of 'doron-limit' to facilitate this great development.
It is not 'doron-limit' but simply 'limit'.

Let X be a placeholder for that is summed.

If |X - L| = 0 then L is called the limit of X.
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Old 1st May 2015, 12:03 AM   #380
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Originally Posted by Little 10 Toes View Post
Please show someone else's work that mentions "levels" in the place value method.
The validity of notions is independent of the amount of those who understand them.
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Old 1st May 2015, 12:14 AM   #381
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Originally Posted by jsfisher View Post
I have no idea what you mean. It handles, for example, infinite series quite well.
You indeed have no idea, exactly because
Originally Posted by jsfisher View Post
...determining the limit of the sequence of partial sums does not involve infinity at any step.
Some example: determining the limit of (0.910, 0.9910, 0.99910, ...) actually prevents the understanding that the sum over |N| terms in (0.910, 0.0910, 0.00910, ...) < 1 without 0.000...110 (which is rigorously explained in terms of the relativity between different transfinite cardinals in http://www.internationalskeptics.com...&postcount=347).
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Old 1st May 2015, 02:40 AM   #382
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Originally Posted by doronshadmi View Post
0.333... < 1/3 x
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Old 1st May 2015, 06:44 AM   #383
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Originally Posted by doronshadmi View Post
0.333... < 1/3 x, so your example does not work.
Please provide proof that .333333... < 1/3.

Please answer the first request as well.
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Old 1st May 2015, 06:45 AM   #384
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Originally Posted by doronshadmi View Post
The validity of notions is independent of the amount of those who understand them.
That was not the request. Please try again.
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Old 1st May 2015, 07:36 AM   #385
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Originally Posted by Little 10 Toes View Post
Please provide proof that .333333... < 1/3.
Already given in http://www.internationalskeptics.com...&postcount=379.
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Old 1st May 2015, 07:40 AM   #386
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Originally Posted by Little 10 Toes View Post
Please show someone else's work that mentions "levels" in the place value method.
Why do you think that is important?

Again, http://www.internationalskeptics.com...&postcount=363 is very simple and can be understood by any one.
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Old 1st May 2015, 10:41 AM   #387
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Originally Posted by doronshadmi View Post
No it doesn't. That post does not show anything about 1/3 or 0.333...
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Old 1st May 2015, 10:45 AM   #388
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Originally Posted by doronshadmi View Post
Why do you think that is important?

Again, http://www.internationalskeptics.com...&postcount=363 is very simple and can be understood by any one.
It's important because you like to make your own definitions of existing words. In addition, your post does not make it clear. I can say that 1 is on a higher level than 10 because it's closer to 0.

9 is a higher level than 8 because 8 < 9.

Please define doron-limit.
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Old 1st May 2015, 02:13 PM   #389
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Originally Posted by Little 10 Toes View Post
No it doesn't. That post does not show anything about 1/3 or 0.333...
That post uses a definition that gets rid of the failure of the standard definition that according to it 0 < |an - L| AND (0.999...10 = 1 OR 0.333...10 = 1/3).

The needed details are provided in http://www.internationalskeptics.com...&postcount=358.
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Old 1st May 2015, 02:20 PM   #390
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Originally Posted by Little 10 Toes View Post
I can say that 1 is on a higher level than 10 because it's closer to 0.
My post is vary clear because it uses only absolute values of the place value method, such that 0 is the lowest level that does not contribute anything to a given sum.

Please look at http://www.internationalskeptics.com...&postcount=348.
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Old 1st May 2015, 03:56 PM   #391
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Originally Posted by doronshadmi View Post
My post is vary clear because it uses only absolute values of the place value method, such that 0 is the lowest level that does not contribute anything to a given sum.
Some typographic errors are more amusing than others.
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Old 1st May 2015, 08:18 PM   #392
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Originally Posted by doronshadmi View Post
That post uses a definition that gets rid of the failure of the standard definition that according to it 0 < |an - L| AND (0.999...10 = 1 OR 0.333...10 = 1/3).

The needed details are provided in http://www.internationalskeptics.com...&postcount=358.
A post that refers to other posts. Typical. Are you denying that 1/3 = .333... ?

Please tell me what is the result of:
____
3)1.0


Show your work.

Edit : Sorry, I don't know how to show the long division sign. I'm trying to figure it out in LaTeX.
Edit2: It seems I can't see LaTeX.

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Old 1st May 2015, 09:05 PM   #393
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Originally Posted by doronshadmi View Post
My post is vary clear because it uses only absolute values of the place value method, such that 0 is the lowest level that does not contribute anything to a given sum.

Please look at http://www.internationalskeptics.com...&postcount=348.
"It uses only absolute values of the place value method, such that 0 is the lowest level that does not contribute anything to a given sum."

That still does not make any sense. What sum? You still have not defined doron-level. Please try to define it. Don't give examples.
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Old 2nd May 2015, 12:00 AM   #394
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Originally Posted by jsfisher View Post
Some typographic errors are more amusing than others.
I ma glad that you are amused.

After that, all you need is to open your mind to http://www.internationalskeptics.com...&postcount=379.
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Old 2nd May 2015, 12:06 AM   #395
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Originally Posted by Little 10 Toes View Post
Please try to define it.
Please try to understand http://www.internationalskeptics.com...&postcount=363 by keeping in mind that 0 is the smallest sum.
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Old 2nd May 2015, 05:10 AM   #396
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Yeah, Little 10 Toes, it is all your fault for not understanding doronshadmi's gibberish...just like everyone else.
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Old 2nd May 2015, 07:25 AM   #397
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Originally Posted by jsfisher View Post
Yeah, Little 10 Toes, it is all your fault for not understanding doronshadmi's gibberish...just like everyone else.
Yeah, jsfisher, now you ignore http://www.internationalskeptics.com...&postcount=379.
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Old 2nd May 2015, 07:36 AM   #398
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Originally Posted by doronshadmi View Post
It was not ignored. It was discounted. You posting disjoint thoughts with no logical connection among them does not obligate anyone else to respond to your individual posts.

Why not simply tell us what you'd like your own private definition for limit (we'll call it 'doron-limit') to be? Surely at some point in your life-long quest to overturn Mathematics you will be able to define something. Why not this for a start?
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Old 2nd May 2015, 04:28 PM   #399
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Originally Posted by Little 10 Toes View Post
A post that refers to other posts. Typical. Are you denying that 1/3 = .333... ?

Please tell me what is the result of:
____
3)1.0


Show your work.

Edit : Sorry, I don't know how to show the long division sign. I'm trying to figure it out in LaTeX.
Edit2: It seems I can't see LaTeX.
Originally Posted by Little 10 Toes View Post
"It uses only absolute values of the place value method, such that 0 is the lowest level that does not contribute anything to a given sum."

That still does not make any sense. What sum? You still have not defined doron-level. Please try to define it. Don't give examples.
Originally Posted by doronshadmi View Post
Please try to understand http://www.internationalskeptics.com...&postcount=363 by keeping in mind that 0 is the smallest sum.
So, by the following two posts and the lack of response to my questions, it appears that you don't know how to do long division, and cannot or will not define "doron-level" (meaning they way that you use the word limit). And why do we care about why you think that 0 is the smallest sum? You still believe that 0.00...1 is still a number.

Last edited by Little 10 Toes; 2nd May 2015 at 04:29 PM.
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Old 3rd May 2015, 04:46 AM   #400
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Originally Posted by jsfisher View Post
You posting disjoint thoughts with no logical connection among them
Please support your argument in details, according to http://www.internationalskeptics.com...&postcount=379 content.
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