Final 0.999... question I promise

[Bob Brown MSEE]

Then it is false to equate ...0003 to 3

In my system \(\displaystyle \overline{0}3\) is the only expression that does represent 3/1.
This subtraction is allowed by the arithmetic defined. You refuse to use it because your intuition tells you that it will fail (notions about infinity). But when you did use it, you found my system internally consistent.
It is difficult to stop using tautology.

 

[mackdaddy]

I am not being disrespectful to anyone. Mack himself has pointed out that he is in 9^thgrade, which means he is about 14, an age that is certainly not adult. Presumably, he has not yet studied geometry, I am currently in pre-AP Geometry Math team, ranked 2nd state wide in division 2 geometry math team, and completely understand what a formal proof is, even though I am 14
where students are introduced to formal proofs. He has not studied calculus, where students are introduced to a little bit of standard analysis. He presumably has not studied abstract algebra, where students are introduced to a formal presentation of the real number system. Given where these threads have wandered, it would be surprising if he were not confused. He certainly seems to be confused because he claims not to understand the relatively simple reasoning that leads within standard analysis to 0.999... = 1.000... If he is not confused and is simply “messing with me,” then he has succeeded.
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I am saying that ...66667 is meaningless within the standard definitions of infinity and infinitely repeating decimals because there is no last digit in terms of those definitions. I have no idea what an infinitely repeating decimal would be under an alternative definition of infinity. For all I know, it may follow from such a definition that ...66667 is well defined and exactly equals 1/3. But under the definitions that are generally accepted ...66667 is an approximation to 2/3.
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I certainly did not intend to misquote anyone, nor do I think I have. You asked someone to comment on ...66667 = 1/3:
.

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I disagree with that statement (at least in terms of the standard conventions of mathematics.) Nor do I think it helps Mack understand the logic that leads to 1.000... = 0.999... Actually if it was agreed upon that 0.6...6667 is equal to 2/3, then it also allow for there to be a difference of 0.0...0001 between 0.999... and 1. But since this is not agreed upon by everybody you are absolutely right it does not help me in any way. Also it's not that I don't understand the logic behind the statement that 0.999...=1, I understand and agree with this logic, but I have a wonderful thing called an open mind, and I also understand the counter-arguments possible to this claim.

So please understand, I am not outright doubting you're logic, but simply trying to view this from a different stand-point. This in turn will hopefully enlighten me in a broader spectrum than just thinking about how 0.999... IS equal to 1. I've already thought about HOW SO, but now I am thinking about HOW NOT. And I am sorry if I have pushed your button too far.

 

[lookagain]

I hadn't planned on posting again in this thread until I received this PM:

Sorry if I hurt your feelings -- it was not intentional

I believed that you were a heavy hitter from your posts.
I assumed that if anyone on this board understood p-adic fields, it would be you.
I feel a little guilty, because I invited you to join-in. I wasn't aware that you are weak in this area. Please accept my apologies for any embarrassment that you may have suffered.
​

- - - combined with - - -​

In my system \(\displaystyle \overline{0}3\) is the only expression that does represent 3/1.

"my system!?" You mean your fabricated system where you state that certain expressions mean
something that they don't. The discussion of your "system" went off-track" from the OP's question.
And then there's JeffM, me, (who else?) who tried to rationalize with your "system." Your "system"
could be addressed in its own thread under "Odds and Ends." I got suckered into the discussion
with your "system" until I realized it wasn't addressing the OP's question, which was addressed
by already established systems.

 

[mackdaddy]

I hadn't planned on posting again on this thread until I received this PM:

​

Whatever it is it's not loading on my computer.

 

[mackdaddy]

And also, a PERSONAL message is personal and not public, so how inconsiderate of you to post that, and also this thread was not opened to act as a place for exchanging rude immature statements, on others math skills. And if you thought it was, I'm sorry, but it wasn't. And Bob Brown was thoughtful enough to send this in a personal message which you have now, without practical reason have made public.

 

[lookagain]

And also, a PERSONAL message is personal and not public, so how inconsiderate of you to post that, and also this thread was not opened to act as a place for exchanging rude immature statements, on others math skills. And if you thought it was, I'm sorry, but it wasn't. And Bob Brown was thoughtful enough to send this in a personal message which you have now, > > without practical reason have made public. < <

You can go on about your business. And, based on his history, the positive intent of sincerity and lack of arrogance just aren't there.

Never, ever state that there was without a practical reason for what I did. Get rid of your
presumptions about me.

(The following had been directed to macdaddy in a prior post.)

I do not believe that there is yet much feeling of wasting time. However, as you continue to resist proof,
you will start to look like a troll.

 

[mackdaddy]

OK OK I'm sorry, I just didn't want any fights to arouse because of this stupid math post. I mean it's math, and trust me I'm all about math, but it's not worth getting worked up about it.

 

[Bob Brown MSEE]

"my system!?" You mean your fabricated system where you state that certain expressions mean
something that they don't. The discussion of your "system" went off-track" from the OP's question..

The phrase "my system!?" refers to the link = #17
It defines precisely what I mean when I say Repeating Integer Decimals.

I believe that I was completely motivated by the OP's question and HIS lead in the discussion,
Since Mackdaddy IS the OP, I believe that he can speak for himself.


If I offended anyone I apologize. If you (Lookagain) want to publish a private message to you from me, I give you that permission (after the fact). If we can follow Mack's advice (in his thread) and get back to objective arguments, then I am sure the OP's needs will have been met.

 

[Bob Brown MSEE]

In a "Forum", I usually avoid any argument that depends upon a reference to authority. The advantage of exchange is cross-examination. Statements like "It's not logical to set ...6667 = n, because n isn't a finite number." or "Nonstandard" or "common meaning" WITHOUT submitting to logical cross-examination OR references, are not useful.

I found a reference; this might be more valuable than cross-examination in this environment. I prefer to be logically cross-examined, but that is difficult without dialog. The OP says that he learned something about keeping an open mind. That makes this thread extremely valuable.



I suppose that Wolfram would disagree if I tried to tell them that it is improper and non-standard to describe Rationals as an infinite sum of (in my notation digits) values, each greater than 1 in value.

 

[Bob Brown MSEE]

P-adic numbers in a new thread

Hi Mac,

Lookagain suggested that I take the p-adic portion of this discussion to another thread.
If you were interested you can follow it on Odds & Ends.