1 is 0.9999999999999............

[Pete]

I may have agreed in post 83 but have since spent many post showing that I actually disagree.

Yes. And I think it's plain that you're mistaken.

Look, this is really indisputable:

10 x 0.999... = 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...
9 x 0.999... = 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...

Agreed?

And obviously:
0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... - 0.999... =
0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...

Right?

 

[Quantum Quack]

He just proved you wrong. So did I.

but Tach all Underfined is saying is that the extended digit doesn't exist yet is present regardless... zero.....which further states that the infinite string has resolved to the infinitesimal

 

[Tach]

Hi Pete.

With respect I must disagree with your unexplained "moving the decimal point one place to the right".

This is the definition of a multiplication by 10 of a periodic number. They teach that in high school:

10*0.(N)=N.(N) for ANY N.

I would humbly suggest that fundamentally that is the consequence of extending the number string itself (irrespective of parsing to begin with) such that the leading 9 in 0.999... is FORCED to move to the left across the decimal point 'parsing' notation used for the string overall.

Your "suggestion" is contradicted by basic arithmetic.

In short, there is no basis for just 'moving the decimal point', since the decimal point is a NOTATION element, not an effective part of the number string/operation of multiplication by 10 itself

Basic arithmetic books contradict your (fringe/incorrect) claims, 10*0.(N)=N.(N) for ANY N.

 

[Tach]

but Tach all Underfined is saying is that the extended digit doesn't exist yet is present regardless... zero.....which further states that the infinite string has resolved to the infinitesimal

Undefined espouses a lot of fringe misconceptions (such as "zero is not a number", "0.999... is not a number"), etc. I just shown his newest claim to be false, exactly as his other claims. So did Pete.

 

[Quantum Quack]

Yes. And I think it's plain that you're mistaken.

Look, this is really indisputable:

10 x 0.999... = 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...
9 x 0.999... = 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...

Agreed?

And obviously:
0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... - 0.999... =
0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...

Right?

so
all you are trying to saying is that
9.999... - 0.999... = 9
so therefore
9 x 0.999 = 9
yes?

If so no, I don't agree because in the second instance a 1/infinity needs to be added for the sum to be 9

9 x 0.999... + 1/infinity = 9
the use of the infinitesimal is because we are inverting the proof. [ as suggested earlier with the brick and the infinite slices. thought experiment ]
Highlighting the difference between subtraction and addition of infinities...
As suggested with the brick gedanken subtracting infinities is easy but adding them is a totally different case.

 

[Undefined]

Looking at it that way, moving the decimal point is a consequence of multiplying by ten.
Adding a zero to the end of an integer multiplied by ten is a similar consequence.

"Extending the number string" is not multiplication by ten, it's not a math operation at all. It's a parsing operation in exactly the same way as shifting the decimal point.

Again I beg to differ, mate. The operation of multiplication by "10" effectively brings a "0" TO the operation. That is the fundamental aspect being inadvertently hidden by all the other higher level abstract symbolic manipulations I and QQ have spoken of.

The moving of a decimal point in any direction IS mere empty manipulation of FORMAT; whereas the bringing of a "0" ELEMENT to the end of the element string (ending or unending as the case may be to begin with) is an OPERATIONALLY RELATABLE action TO that notation because that is the only place that a "0" brou8ght to the operation CAN go IF you multiply by 10 which contains THE "0" which that notation format PUTS at the END of the string so operated upon BY that 10 factoe containing a '0" element to go somewhere IN that string (and it's not at the front of that string, so it can only be at the rear of that string).

That is my observation of the fundamental actions involved, irrespective of whatever other FURTHER assumptions from expression 'formatting' or math axiom 'rules' may be brought 'trivially' to the consideration of what is actually happening in the operation in reality.

That is only my opinion/observation from the most fundamental level before all the sophisticated 'treatments' assumptions brought in afterwards, of course. Thanks Pete, QQ, everyone, for your polite discourse in the matter.

 

[Tach]

so
all you are trying to saying is that
9.999... - 0.999... = 9
so therefore
9 x 0.999 = 9
yes?

Yep, you got it.

 

[Tach]

Again I beg to differ, mate. The operation of multiplication by "10" effectively brings a "0" TO the operation. That is the fundamental aspect being inadvertently hidden by all the other higher level abstract symbolic manipulations I and QQ have spoken of.

Nope, 10*0.(N)=N.(N) for ANY N.

 

[Pete]

Again I beg to differ, mate. The operation of multiplication by "10" effectively brings a "0" TO the operation.

No, that idea is a hangover from learning to multiply integers by ten.

 

[Pete]

so
all you are trying to saying is that

No, that's the next part of the proof. We're still addressing this bit:
10 x 0.999... - 0.999... = 9 x 0.999...

I really need you to explicitly address these simple equations:
10 x 0.999... = 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...
Do you agree?

9 x 0.999... = 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...
Do you agree?

0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... - 0.999... =
0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...
Do you agree?

 

[Quantum Quack]

No, that's the next part of the proof. We're still addressing this bit:
10 x 0.999... - 0.999... = 9 x 0.999...

I really need you to explicitly address these simple equations:
10 x 0.999... = 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...

9 x 0.999... = 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...

Agreed?

And obviously:
0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... - 0.999... =
0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...

Right?

Sorry to say, Pete but until the issue of what 0.999... + 0.999... equals is resolved it would be a silly exercise
So let's clarify the situation...best to work out a simple one to start with

What does 0.999... + 0.999... equal ?
1.99999999999...8 or
does it equal 2
and before you answer 2, remember you can not use an unproven proof to prove the unproven proof.

 

[Undefined]

He just proved you wrong. So did I.

Tach, you've been warned by the mods before about 'declaring/prejudicing' and otherwise misconstruing the discussion 'result' even before the discussion is complete.

I pointed out where in my observation his 'proof' is of the trival kind based on convention/definition, not on the fundamentality involved which bring into question those very same conventions/definitions which tend to build up and 'hide' the fundamentalities involved at its most basic level to begin with before the abstractions and trivial manipulations set in.

So please stop trying to 'control' and 'prejudice' the discourse conclusions by 'declaring victory' and/or 'declaring proven' etc before the discussion is complete. Thanks.

This is the definition of a multiplication by 10 of a periodic number. They teach that in high school:

10*0.(N)=N.(N) for ANY N.




Your "suggestion" is contradicted by basic arithmetic.



Basic arithmetic books contradict your (fringe/incorrect) claims, 10*0.(N)=N.(N) for ANY N.

Yes, by DEFINITION according to axioms being brought into question NOW. So a definition is not an 'operation' which is more fundamantal than the axiomatic assumption/definition you present as the trivial 'proof' for something that is yet to be decided in THIS discussion.

Again, that is an assertion from axioms/trivial manipulation of symbols and numbers in mixed context (as already explained by QQ).

So please stop with your trivial repetition of axiomatic trivialities as 'proofs' etc. The discussion has not yet completed, and those trivial 'proofs' and 'axioms' etc are what is being brought into question IN this discussion. So no more circuitous and self-referencing 'rote-learned' retorts that mean nothing in the context we are discussing those things in. Thanks.

Undefined espouses a lot of fringe misconceptions (such as "zero is not a number", "0.999... is not a number"), etc. I just shown his newest claim to be false, exactly as his other claims. So did Pete.

Without giving the full context and understandings/arguments brought in support of those comments I made elsewhere, you are TROLLING and making obviously personal disparagements based on YOUR own misconstruings out of full and proper contexts.

Please STOP trolling and personalizing this thread/discussion, Tach. Else I will have no option but to report you for it. Thanks.

 

[Pete]

No. Stop stalling, answer the easy questions.

10 x 0.999... = 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...

Yes or No?

 

[Quantum Quack]

No. Stop stalling, answer the easy questions.

10 x 0.999... = 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999...

Yes or No?

No is the only answer I can give.
because you have not shown that 0.999... can be added effectively to begin with.
the difference between adding and multiplying infinite strings is being high lighted.
I could say yes but you will know I would be lying if I did so...
Do you want me to say yes or not?

If so, yeah sure the equation IMO is sound... no problemo...

If you want me to lie then by all means accept the lie...
I suppose Zeno of Elea was lying too...when he proposed that a paradox associated with zero existed.

Heisenberg must be lying as well.. with the uncertainty principle... etc

 

[Pete]

No is the only answer I can give.

Then we are at an impasse.
Repeated addition is the definition of multiplication. If you don't accept it, then no one (including yourself) knows what you are talking about when you talk about multiplication.

Try this:
$$2 \pi = \pi + \pi$$
True or false?

 

[Undefined]

No, that idea is a hangover from learning to multiply integers by ten.

Whereas your "moving the decimal point to the right" was not some hangover from an even less fundamentally based 'learning' convention?

Seriously, the additional "0" brought BY the "10" number string has to go somewhere, and that is at the end of whatever string is being operated on and extended BY that 10 multiplication operation.

It is more fundamental in every way (including format or learning device) that the "0" adds to the string at the right end irrespective of the decimal extent/format of that string.

See what I'm getting at? when we multiply 10 x 10 we move the target 10 to the left FORCED by the additional 10 x operation to be moved from the "tens" place to the "hundreds" place. That is more fundamental than anything involving the decimal point which does not even enter the operation/notation at all in this case (unless you TRIVIALLY notate the original elements as 10.00 x 10.00 which trivially includes the extended decimal notation unnecessarily because it is not fundamentally required in that case).

That's all I am observing, from a more fundamental level than the trivial cross-contextual manipulatory overlays which have been put on such otherwise straightforwardly comprehensible fundamentals. Thanks for listening to my opinions/observations on the matter as it is being presented/discussed in context so far, mate!

 

[Quantum Quack]

Then we are at an impasse.
Repeated addition is the definition of multiplication. If you don't accept it, then no one (including yourself) knows what you are talking about when you talk about multiplication.

Try this:
$$2 \pi = \pi + \pi$$
True or false?

sure..true, yes... but the digits of pi are not identical as infinite repeaters so I am not convinced you know what you are talking about either...
try something that relates to the topic instead...

 

[Pete]

Whereas your "moving the decimal point to the right" was not some hangover from an even less fundamentally based 'learning' convention?

No, moving the decimal point is more fundamental. Adding a 0 is a consequence of moving the decimal point.
Every terminating decimal is actually followed by infinite zeros:
7 = 7.000...

Multiplying by ten doesn't add a zero on, it just moves one of those zeros over to where we can see it:
7 x 10 = 70.000...

Seriously, the additional "0" brought BY the "10" number string

There is no additional zero. That is an illusion. You're taking the lessons you learned as a 6 year old way beyond their useful domain.

 

[Quantum Quack]

@ Pete,
I am asking that instead of tackling the entire addition sequence that we merely attempt one step, and you call this an impasse. The impasse is not to do with mathematics.


0.999... +0.999... = ?

 

[Pete]

sure..true, yes... but the digits of pi are not identical as infinite repeaters so I am not convinced you know what you are talking about either...
try something that relates to the topic instead...

The simple definition of multiplication is repeated addition. If you don't accept that, then I don't know what you mean when you talk of multiplication.

By definition:
2 x 0.999.. = 0.999... + 0.999...

Do you agree?