If you notice that $$9x=(10-1) \sum_{k=1}^{\infty} \frac{9}{10^k}$$ you get $$9x=9$$ in one step.
1 is 0.9999999999999............
- Thread starter chinglu
- Start date
If you notice that $$9x=(10-1) \sum_{k=1}^{\infty} \frac{9}{10^k}$$ you get $$9x=9$$ in one step.
Motor Daddy
Valued Senior Member
Correct, I will never accept that 99.999...%=100%. Never!
x=.999...
10x=.999...+.999...+.999...+.999...+.999...+.999...+.999...+.999...+.999...+.999...
10x-x=.999...+.999...+.999...+.999...+.999...+.999...+.999...+.999...+.999...
9x=.999...+.999...+.999...+.999...+.999...+.999...+.999...+.999...+.999...
Does 1=1?
None of this temper tantrum demonstrates that 0.999... ≠ 1 and further...
9x=.999...+.999...+.999...+.999...+.999...+.999...+.999...+.999...+.999...
= ( .999...+.999...+.999... ) + ( .999...+.999...+.999... ) + ( .999...+.999...+.999...)
= ( ( .999... + .999... ) + .999... ) + ( ( .999... + .999... ) + .999... ) + ( ( .999... + .999... ) + .999... )
= ( ( .555... + .444... + .555... + .444... ) + .999... ) + ( ( .555... + .444... + .555... + .444... ) + .999... ) + ( ( .555... + .444... + .555... + .444... ) + .999... )
= ( ( 1.111... + .888... ) + .999... ) + ( ( 1.111... + .888... ) + .999... ) + ( ( 1.111... + .888... ) + .999... )
= ( ( 1 + .999... ) + ( .999... ) ) + ( ( 1 + .999... ) + ( .999... ) ) + ( ( 1 + .999... ) + ( .999... ) )
= ( 1 + ( .999... + .999... ) ) + ( 1 + ( .999... + .999... ) ) + ( 1 + ( .999... + .999... ) )
= 3 + ( 1 + .999... ) + ( 1 + .999... ) + ( 1 + .999... )
= 6 + ( .999... + .999 ) + .999
= 7 + ( .999... + .999 )
= 8 + .999...
= 8 + x
Motor Daddy
Valued Senior Member
Are you saying that .999... can't be added together 9 times? If it can be added together 9 times what is the total? I'll give you a hint: Since the .999... does not have a "1" in the ones position then 9 of them will not equal 9, it will be less than 9. Fact!
There seems to be a lot of proven things that you refuse to accept.
Conversely, there are a lot of things that have been show to be false that you do accept.
That is interesting in a sad uninteresting sort of way....
I have indeed proved that using this proof [ left side] all that is proved is that 0.999... = 0.999...
It is not an issue that mathematics can pseudo calculate 1=0.999... what is at issue is whether it can do so and maintain contextual integrity whilst doing so.
And I have proved that it can not do so..
9x= 9
is the same as saying 9(0.999..) = 9(0.999...)
which is very different to 9(0.999...) = 9(1.000...)
As there is no presumption of proof, that is that 0.999...=1, prior to proof being proved to be true.
To say that the pseudo nature of my use of mathematics somehow inhibits your ability to deduce what I am trying to convey when it is basic and quite simple [ elementary math in fact] is not a good indication of your actual mathematical ability.
I may have only elementary math at best, but one thing I did learn that you may have become complacent about, is that you do not mix the context of what you are doing because if you do the result will invariably be invalid.
In this case contextual integrity is utterly essential for the math to ultimately make sense. { I would strongly recommend that you seriously have a look at just this issue of contextual integrity]
The proof in question, blatantly mixes context and is merely a displaying a clever trick when calculating 0.999...= 1 . It is indeed a fraud and a damn easy one to fall for.
0.999... = 1 CAN NOT be calculated with out mixing context of quantity and value thus any calculated proof is invalid.
Therefore 0.999... = 1 can only be defined.
Once this is acknowledged all this BS arguing with Motor Daddy and millions of other students of Math will cease.
In my opinion Motor Daddy is totally correct when he says that 0.999... can never be calculated to equal 1 as the ...999 just go on for ever. However once he and others are acknowledged for being correct in stating infinity = infinity, the issue of defining the solution using a process of limits comes to the fore. [hence the use of the word "defined".
And suddenly there is nothing more to argue about..
Unless you wish to argue that infinity =/= infinity 'ad nauseum'? But then maybe you all do.?
Hi, Monimonika. 
First, my apologies if my post inadvertently offended you. Not my intention at all. Sorry.
My intention was to, generally observe that:
- due diligence in assessing the background context to a discussion/side-discussion would help obviate cross-purpose exchanges and misunderstandings;
- the main point of the discussion has eventually arrived at the reality-versus-maths operations involving numbers/divisions etc.; and to demonstrate the point at issue, the REAL PIE disc was earlier introduced by MD as a test for all the arguments about what is a fraction with repeating decimals 'in reality' (as opposed to the maths based 'limits result' long already covered); and
- the TRIVIAL arguments/examples have all been made ad nauseam, so NOW we should all concentrate on the ESSENTIALS of the FRACTION of 1/3 etc (and not keep reverting back to maths-based trivial constructions which are then equally trivially 'deconstructed' to 'prove' some trivial effectively NON-action, as mentioned already).
That was all I was trying to get across to you and everyone at this juncture in such discussions:
Due diligence to prevent repeated cross-purpose/misunderstandings exchanges (which usually lead to 'emotional exchanges' born of frustration/repetition on both 'sides').
The discussion has reached the MATHS-versus-REALITY treatments of the 'point' concept/entity (hence MD's real pie he introduced earlier).
Avoiding the usual and now-oft-presented (here and elsewhere) trivial 'proofs' and 'exercises which only leave more questions to answer in this context NOW.
Again, sorry if I came across as offensive to you personally. Not my intention.
Be cool, keep up the discourse and good luck and good thinking to you and everyone, Monimonika, everyone!
Keep up the discourse
First, my apologies if my post inadvertently offended you. Not my intention at all. Sorry.
My intention was to, generally observe that:
- due diligence in assessing the background context to a discussion/side-discussion would help obviate cross-purpose exchanges and misunderstandings;
- the main point of the discussion has eventually arrived at the reality-versus-maths operations involving numbers/divisions etc.; and to demonstrate the point at issue, the REAL PIE disc was earlier introduced by MD as a test for all the arguments about what is a fraction with repeating decimals 'in reality' (as opposed to the maths based 'limits result' long already covered); and
- the TRIVIAL arguments/examples have all been made ad nauseam, so NOW we should all concentrate on the ESSENTIALS of the FRACTION of 1/3 etc (and not keep reverting back to maths-based trivial constructions which are then equally trivially 'deconstructed' to 'prove' some trivial effectively NON-action, as mentioned already).
That was all I was trying to get across to you and everyone at this juncture in such discussions:
Due diligence to prevent repeated cross-purpose/misunderstandings exchanges (which usually lead to 'emotional exchanges' born of frustration/repetition on both 'sides').
The discussion has reached the MATHS-versus-REALITY treatments of the 'point' concept/entity (hence MD's real pie he introduced earlier).
Avoiding the usual and now-oft-presented (here and elsewhere) trivial 'proofs' and 'exercises which only leave more questions to answer in this context NOW.
Again, sorry if I came across as offensive to you personally. Not my intention.
Be cool, keep up the discourse and good luck and good thinking to you and everyone, Monimonika, everyone!
Keep up the discourse
Fifty pages! I think this deserves some kind of recognition. A plaque somewhere, perhaps?
Or have I misspelled that?
Or have I misspelled that?
It is really stupid I think that:
Motor Daddy is arguing that infinity = infinity
and others are arguing that infinity=/= infinity.
Lunacy prevails
Motor Daddy is arguing that infinity = infinity
and others are arguing that infinity=/= infinity.
Lunacy prevails
yeah but sometimes an intractable issue like this one that has plagued billions of math students for centuries takes time to work out. [might go to 100 pages ... who knows? and if not another thread will start up somewhere else and the "cosmic ballet" continues...]
Hi everyone.
Just to point out that we have reached the stage of comparing the reality-versus-maths treatments/concepts of point.
To this end, MD has put the example of a REAL PIE which is (supposedly, as claimed by some) amenable to EXACT DIVISION into 3 equal parts'.
Well, we have the mathematical 'operation' that the central 'point' of no dimensional extent can be so 'divided' (or partitioned) endlessly etc.
HOWEVER we still have no example of a real 'process' which can actually divide MD's REAL PIE DISC into three equal parts!
Simply because no real process has been offered by the mathematicians to do this WITHOUT assuming a CENTRAL POINT OF NO DIMENSIONAL extent whatsoever!
Now IF we do treat a real pie as having central point which is occupied by real PIE material, then what? How do we divide that central REAL MATERIAL to arrive at a 'settled' partition EQUALLY?
That is the question NOW before us. We know what the mathematical treatment/concept of that 'point' is; but what is the reality treatment insofar as actually diving that one central point equally into three for each of the three sectors of real pie?
Thanks for all your discussion so far, everyone. Stay cool and enjoy the comparative maths-reality discourse! Cheers.
Just to point out that we have reached the stage of comparing the reality-versus-maths treatments/concepts of point.
To this end, MD has put the example of a REAL PIE which is (supposedly, as claimed by some) amenable to EXACT DIVISION into 3 equal parts'.
Well, we have the mathematical 'operation' that the central 'point' of no dimensional extent can be so 'divided' (or partitioned) endlessly etc.
HOWEVER we still have no example of a real 'process' which can actually divide MD's REAL PIE DISC into three equal parts!
Simply because no real process has been offered by the mathematicians to do this WITHOUT assuming a CENTRAL POINT OF NO DIMENSIONAL extent whatsoever!
Now IF we do treat a real pie as having central point which is occupied by real PIE material, then what? How do we divide that central REAL MATERIAL to arrive at a 'settled' partition EQUALLY?
That is the question NOW before us. We know what the mathematical treatment/concept of that 'point' is; but what is the reality treatment insofar as actually diving that one central point equally into three for each of the three sectors of real pie?
Thanks for all your discussion so far, everyone. Stay cool and enjoy the comparative maths-reality discourse! Cheers.
Hi everyone.
Just to point out that we have reached the stage of comparing the reality-versus-maths treatments/concepts of point.
To this end, MD has put the example of a REAL PIE which is (supposedly, as claimed by some) amenable to EXACT DIVISION into 3 equal parts'.
Well, we have the mathematical 'operation' that the central 'point' of no dimensional extent can be so 'divided' (or partitioned) endlessly etc.
HOWEVER we still have no example of a real 'process' which can actually divide MD's REAL PIE DISC into three equal parts!
Simply because no real process has been offered by the mathematicians to do this WITHOUT assuming a CENTRAL POINT OF NO DIMENSIONAL extent whatsoever!
Now IF we do treat a real pie as having central point which is occupied by real PIE material, then what? How do we divide that central REAL MATERIAL to arrive at a 'settled' partition EQUALLY?
That is the question NOW before us. We know what the mathematical treatment/concept of that 'point' is; but what is the reality treatment insofar as actually diving that one central point equally into three for each of the three sectors of real pie?
Thanks for all your discussion so far, everyone. Stay cool and enjoy the comparative maths-reality discourse! Cheers.
no we haven't
we haven't even got close to working in the real world.
the issue is about 0.999... = 1 and why this is so controversial. A pure math exercise and not a lot to do about reality. [not yet any way]
The bottom line is that we have a flawed approach to teaching this aspect of calculus, where by on one hand we state we can calculate the result and on the other we say we can't calculate the result.
Using and publishing flawed algebraic proofs doesn't help either and in fact undermines genuine mathematics terribly. IMO
Mr. Quack I agree with you wholeheartedly. The Internet-wide confusion about .999... does indeed represent a failure of our schools to properly teach the subject; or rather, many subjects. The distinction between math and the real world. The nature of the real numbers. The meaning of decimal notation.
But in these endless threads, no matter how carefully people try to explain these concepts, it never seems to help; and only serves to take the discussion in ever more strange and pointless (no pun intended) directions.
That, I do not understand.
MD, the Quack, Undefined, they are all struggling with this simple notion. 50 pages and they STILL do not get it.
So, you think that using addition instead of subtraction convinced him? Look again!
Simple. We bake the pie in such a way that the total number of atoms is a multiple of 3. For example, if we back a 3 mole pie, then each slice will contain one mole of pie.
Alternatively, we change the way we cut the pie so that we avoid having to split the central pie in three. A pie, after all, can be gut into three pieces with two cuts. Then the only question you're left with is which side of the cut individual pie atoms need to be on to give equal areas.
I know, I already pointed that out to you. Tough.
Oh yea, this from the guy/fellow that just got banned/booted for being so obusive/offensive.
Agrees...
It is truly amazing how a "subtle fraud" can be so effective in destabilizing an entire profession for hundreds of years.
The error in context leads teachers and students to mistakenly believe that the subject they are studying [Calculus] is not really needed. After all they may mistakenly ask, why have calculus if elementary math will do?
The famous proof may eventually become an "infamous proof" of how easy it is to be deceived by a simple, subtle yet incredibly influential loss, of contextual integrity.
Change will happen though as the nature of the beast [www] is utilized to promote it.
I already have forwarded parts of this threads discussion to various university departments for their erudite assessment.
"You too can help by asking your professors to confirm contextual integrity within the said proof."
Once enough senior people know of it and have found it for them selves, it will be withdrawn as a proof of 0.999...= 1 and re posted as a proof of how easy it is to be fuddled.