Cont: Deeper than primes - Continuation 2

[zooterkin]

Since you mentioned it, here she is; fast-talker Vi Hart:

9.999... reasons that .999... = 1
https://www.youtube.com/watch?v=TINfzxSnnIE

Doron, pay particular attention to Reason 6, it's for you!

 

[doronshadmi]

Doron, pay particular attention to Reason 6, it's for you!

zooterkin, pay particular attention that Vi Hart reasoning is restricted to countably infinite cardinality, in this case, so it can't be used in order to say any meaningful thing about my reasoning.

Also please pay attention to the trivial mistakes that Vi Hart is doing in https://www.youtube.com/watch?v=wsOXvQn3JuE exactly because she does not use any base, and again uses only countably infinite cardinality.

 

[zooterkin]

zooterkin, pay particular attention that Vi Hart reasoning is restricted to countably infinite cardinality, in this case, so it can't be used in order to say any meaningful thing about my reasoning.

Please explain exactly what is wrong with her reasoning.

Also please pay attention to the trivial mistakes that Vi Hart is doing in https://www.youtube.com/watch?v=wsOXvQn3JuE exactly because she does not use any base, and again uses only countably infinite cardinality.

You are aware that's an April Fools video, aren't you?

 

[doronshadmi]

Please explain exactly what is wrong with her reasoning.

You are aware that's an April Fools video, aren't you?

Yes, I am aware of it, and it does not change the fact that not using base leaves her stuff with undefined notations, exactly as done in https://www.youtube.com/watch?v=TINfzxSnnIE&feature=youtu.be&t=272 .

Again, Vi Hart reasoning is restricted to countably infinite cardinality, in this case, so it can't be used in order to say any meaningful thing about my reasoning.

 

[zooterkin]

Yes, I am aware of it, and it does not change the fact that not using base leaves her stuff with undefined notations, exactly as done in https://www.youtube.com/watch?v=TINfzxSnnIE&feature=youtu.be&t=272 .

In maths, and every day life, base 10 is assumed unless otherwise specified.

Again, Vi Hart reasoning is restricted to countably infinite cardinality, in this case, so it can't be used in order to say any meaningful thing about my reasoning.

Please explain why, rather than just restating.

 

[jsfisher]

That's a bit too coarse an explanation and therefore not quite correct.

Sure, I'll accept that. It did seem appropriate, though, for the audience I intended.

 

[doronshadmi]

In maths, and every day life, base 10 is assumed unless otherwise specified.

Unless you are using a reasoning where base is significant.

Please explain why, rather than just restating.

http://www.internationalskeptics.com/forums/showpost.php?p=10663593&postcount=596 and all the links that follows from within it.

And please do not follow after Little 10 Toes, because you will get nowhere in this discussion.

 

[jsfisher]

Yes, I am aware of it, and it does not change the fact that not using base leaves her stuff with undefined notations

Are you really going to cling to that? She didn't say "base 10", Oh, Noes!!!!! Seriously, if that's the best you got as a counter-argument, you need to reconsider your position.

And I've said, since you've failed to declare your notational basis and your symbol set, your notations are equally undefined.

 

[doronshadmi]

Are you really going to cling to that? She didn't say "base 10", Oh, Noes!!!!! Seriously, if that's the best you got as a counter-argument, you need to reconsider your position.

And I've said, since you've failed to declare your notational basis and your symbol set, your notations are equally undefined.

Since you have failed to understand my reasoning about limits (exactly because you are not using bases and your reasoning is restricted only to countably infinite cardinality of the place value method) you have no meaningful thing to say about it.

Stupid games as done by L 10 T (criticized in http://www.internationalskeptics.com/forums/showpost.php?p=10663593&postcount=596) are leading to nowhere.

 

[Slings and Arrows]

Albert H. Lightstone uses a “decimal hyperreal" semicolon notation that is very similar to the 0.000…1 notation:

0.000…;…01

http://en.wikipedia.org/wiki/A._H._Lightstone

Also, here is an interesting article by Karin Katz and Mikhail Katz:

When is .999… less than 1?
http://www.math.umt.edu/TMME/vol7no1/TMME_vol7no1_2010_article1_pp.3_30.pdf

 

[Slings and Arrows]

And here is another interesting article by Karin Katz and Mikhail Katz:

"Zooming in on infinitesimal 1-.9.. in a post-triumvirate era"
http://arxiv.org/abs/1003.1501

I really enjoy reading Mikhail Katz; all of his articles are fascinating:
http://en.wikipedia.org/wiki/Mikhail_Katz

 

[doronshadmi]

Albert H. Lightstone uses a “decimal hyperreal" semicolon notation that is very similar to the 0.000…1 notation:

0.000…;…01

Lightstone's notation is based on non-standard analysis that uses hyperintegers.

My system is simpler, it uses the difference between countably infinite cardinality and uncountably infinite cardinality, in order to define a number like 0.000...1₁₀ > 0, which is used as the complement of number 0.999...₁₀ to 1, such that 0.999...₁₀ = 1 - 0.000...1₁₀.

More details are give in http://www.internationalskeptics.com/forums/showpost.php?p=10663593&postcount=596 and all of its chain of links.

 

[zooterkin]

Lightstone's notation is based on non-standard analysis that uses hyperintegers.

My system is simpler, it uses the difference between countably infinite cardinality and uncountably infinite cardinality, in order to define a number like 0.000...1₁₀ > 0, which is used as the complement of number 0.999...₁₀ to 1, such that 0.999...₁₀ = 1 - 0.000...1₁₀.

Seems a lot of effort when you could just use '0'.

 

[doronshadmi]

Long division has everything to do with your incorrect statement.

What do you get when you divide 1 by 3?

If you divide something by 3, then multiply the result by 3, why do you not have the number you started with?

Is there a reason that you ignored the first question? Can you do long division?

Here is a quote taken from http://www.math.umt.edu/TMME/vol7no1/TMME_vol7no1_2010_article1_pp.3_30.pdf ,page 22:

Question 8.1. Long division of 1 by 3 gives .333… which is a very obvious pattern. Therefore multiplying back by 3 we get .999…=1. There is nothing else to discuss!

Answer. Let us be clear about one thing: long division of 1 by 3 does not produce the infinite decimal .333… contrary to popular belief. What it does produce is the sequence <.3, .33, .333, …>, where the dots indicate the obvious pattern. Passing from a sequence to an infinite decimal is a major additional step. The existence of an infinite decimal expansion is a non-trivial matter that involves the construction of the real number system, and the notion of the limit.

 

[doronshadmi]

Seems a lot of effort when you could just use '0'.

Ye, gray or colors "Seems a lot of effort when you could just use" black or white.

 

[jsfisher]

Here is a quote taken from http://www.math.umt.edu/TMME/vol7no1/TMME_vol7no1_2010_article1_pp.3_30.pdf ,page 22:

Question 8.1. Long division of 1 by 3 gives .333… which is a very obvious pattern. Therefore multiplying back by 3 we get .999…=1. There is nothing else to discuss!

Answer. Let us be clear about one thing: long division of 1 by 3 does not produce the infinite decimal .333… contrary to popular belief. What it does produce is the sequence <.3, .33, .333, …>, where the dots indicate the obvious pattern. Passing from a sequence to an infinite decimal is a major additional step. The existence of an infinite decimal expansion is a non-trivial matter that involves the construction of the real number system, and the notion of the limit.

Highlighting added. Curious, Doronshadmi, that you'd cite a text that promotes the very concept you have so desperately and unsuccessfully fought.

...And per the construction of the real number system and the notion of limit, we arrive at the very conclusion zooterkin would promote: 1/3 = 0.333.... and that 3 x 1/3 = 3 x 0.333... = 0.999... = 1.

Once again, Mathematics ignores Doronshadmi's irrelevant objections.

 

[doronshadmi]

Highlighting added. Curious, Doronshadmi, that you'd cite a text that promotes the very concept you have so desperately and unsuccessfully fought

It is non-curious, jsfisher, that you have missed what you have Highlighted, which is:

The existence of an infinite decimal expansion is a non-trivial matter that involves the construction of the real number system, and the notion of the limit.

The construction of the real number system and the notion of limit can't be trivially defined by forcing the finite on the infinite, as done by the definition of convergence, which enables to define one and only one limit for each one of the infinite sequences like (0.3₁₀, 0.33₁₀, 0.333₁₀, ...) or (0.9_10, 0.99₁₀, 0.999₁₀, ...) that have no more than |N| finite terms, and therefore they are insufficient in order to provide finer results about the real number system or about the richness of the limit concept.

On the contrary, a reasoning that uses at least more than one transfinite cardinality (for example |N| AND |R|) is sufficient in order to provide finer results about the real number system or about the richness of the limit concept.

Once again, the definition of convergence is some particular case (with a loss of generality) of my definition of limits.

You are desperately and unsuccessfully force your partial case as the only possible reasoning about the real number system and the notion of limit.

As a result you are missing also Lightstone's notation that is based on non-standard analysis that uses hyperintegers.

More details about my simpler system (w.r.t Lightstone's system) are given in http://www.internationalskeptics.com/forums/showpost.php?p=10666379&postcount=612 (including all of its links).

You and zooterkin somehow became moderators of The International Skeptics Forums, but you unfortunately do not distinguish between Skepticism and Dogmatism (where Dogmatism is your attitude about the last discussed subject in this thread).

As moderators you have the technical ability to shut me up, to send my posts to AAH etc. , but if you do that it will be by the name of Dogmatism.

Once again, Mathematics ignores Doronshadmi's irrelevant objections.

Once again, Mathematics is not a private property of any authority, so no one (including me and you) enables to speak by the name of Mathematics or use any dogmatic approach about it (as you do, for example, in case of mathematical definitions).

 

[jsfisher]

The construction of the real number system and the notion of limit can't be trivially defined by forcing the finite on the infinite....

Your continued protests are irrelevant. Mathematics has a perfectly fine notion of limit. You do not. Mathematics doesn't care.

In other news, 0.999... continues to be identical to 1.

 

[doronshadmi]

Your continued protests are irrelevant.

...And per the construction of the real number system and the notion of limit, we arrive at the very conclusion zooterkin would promote: 1/3 = 0.333.... and that 3 x 1/3 = 3 x 0.333... = 0.999... = 1.

No dear jsfisher, once again, you can't construct the real number system without transfinite cardinality |R|, so all you have is the trivial conclusion that no term of the sequence (0.3₁₀, 0.33₁₀, 0.333₁₀, ...) > 1/3, and therefore it can be taken as its limit, , but, as clearly written in Karin Katz and Mikhail Katz paper ("Passing from a sequence to an infinite decimal is a major additional step"), one can't deduce the identity of 0.333...₁₀ to 1/3 form this sequence. Moreover even 0.333...₁₀ is limited to transfinite cardinality |N| so, the definition of convergence definitely does not deal with the construction of the real number system.

Mathematics has a perfectly fine notion of limit. You do not. Mathematics doesn't care.

Ye, this sentence maybe used as a nice lullaby song in your community for the past 200 years, but it dogmatically ignores Karin Katz and Mikhail Katz paper ("Passing from a sequence to an infinite decimal is a major additional step") and my work on this subject.

In other news, 0.999... continues to be identical to 1.

Only in the lullaby song of your community for the past 200 years.


In a more poetic way, the definition of convergence "jumps over the rainbow" straight to the trivial limit by ignoring the infinitely many alternative limits that are defined "within the rainbow".

Again, more details about my simpler system (w.r.t Lightstone's system) are given in http://www.internationalskeptics.com/forums/showpost.php?p=10666379&postcount=612 (including all of its links).

 

[jsfisher]

No dear jsfisher...<SNIP>...

You continue to argue to disprove definitions. Definitions are not subject to proof. They are, after all, definitions.

So, complain all you like. Mathematics doesn't care you don't understand.