# 1 = 0.999999999999



## RobynC (Jun 10, 2011)

Is one actually equal to 0.99999.... or is it simply creative semantics to make them seem equal.

The best proof I've ever seen is this one

Step 1: x = 0.99999999...
Step 2: 10x = 9.99999999
Step 3: -x = 0.99999999
Step 4: 9x = 9
Step 5: x = 1

Therefore 1 = 0.9999999999....


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## KingArthur (Feb 2, 2012)

Mathematicians (and paherps those in quantitative disciplines too) might not have problems with these mathematical propositions that you are invoking, but I can assure you that philosophers would definitely have serious problems with them. For a start, metaphyisicians, epistologists, Logicians, language philosophers, and philosophers in the philosophy of science discipline would be outraged by these sort of m-propositions.

Perhaps, if they feel like being generous, they would accept them as approximations. But in a hard-headed mode of philosophysical analysis, such approximations would not pass for sound and conclusive mathematical truths. 

Infact, leaving philosophers aside, in the real world such m-propositions would not stand a chance. Simply, it would be practically unaceptable in many practical circumstances or situations. For example, take a peny out of ten pounds (£10) and what results is £9.99. Without wandering too far to draw a concret example, I have personally encountered several instances where the shopkeeeper resfused to accept a price with a missing penny (ie refused to accept £9.99 for a £10 price.) Practically, it seems that these shopkeepers refused because of the missing penny (£0.01). Also, if you take a penny out of one million pounds you are no longer a millionaire for a very obvious practical reason (£1,000,000 - £0.01 = 999,999.99).

IMPORTANT POINT

Mathematicians must keep 'Absolute Truths' separate from 'Natural Approximations'. They are two fundamentally different things. Philosophers, especially those in the above listed disciplines, rigorously enforce this distinction. The world where we can avoid fractions and the usual associated vagueness is currently a distanced dream, if not completely an impossiblity. I have suggested elsehwere on this PF the need to start looking at the "MATHEMATICS OF 'THE PERFECT FIT'" that governs a 'paraplexed world or universe'.


This explanation is not by me, it is taken from 'physics forum' because I'm not clever enough to explain anything like that but as someone said " The power of knowledge is not in memorising every fact but in finding the answers for questions you stumble upon"


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## sprinkles (Feb 7, 2010)

KingArthur said:


> Mathematicians (and paherps those in quantitative disciplines too) might not have problems with these mathematical propositions that you are invoking, but I can assure you that philosophers would definitely have serious problems with them. For a start, metaphyisicians, epistologists, Logicians, language philosophers, and philosophers in the philosophy of science discipline would be outraged by these sort of m-propositions.


Their problem is that math is math, not philosophy.


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## KingArthur (Feb 2, 2012)

He just wanted to show that answers for this problem are different depending what are you looking for: a practical answer? A mathematically correct answer? Or maybe you just want to think about this problem for eternity like a philosopher would do.


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## viva (Aug 13, 2010)

Wasn't there just a thread about this recently?


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## sprinkles (Feb 7, 2010)

KingArthur said:


> He just wanted to show that answer for this problem are different depending what are you looking for: a practical answer? A mathematically correct answer? Or maybe you just want to think about this problem for eternity like a philosopher would do.


Gödel's Incompleteness Theorem is pretty much the answer for those problems that people like to think about forever.



viva said:


> Wasn't there just a thread about this recently?


There was.


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## Diogenes (Jun 30, 2011)

If this thread reaches as many pages as the other one then humanity is clearly doomed.


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## Angelic Gardevoir (Oct 7, 2010)

Not. This. Thread. Again.


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## C6RUSA (Sep 6, 2011)

viva said:


> Wasn't there just a thread about this recently?


yeah, who's the jackass that started that other thread?









But this time I've figured out the real answer ... the answer is 42.

Have a nice day!


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## MetaData (Jan 22, 2012)

Step three starts a yelling match inside my head and step four forces my face to contort into all sorts of unnatural expressions.
X cannot equal 0.999 and -0.999 at the same time, nor does 9*.9999 = 9
Now my head hurts.


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## bellisaurius (Jan 18, 2012)

@MetaData


> X cannot equal 0.999 and -0.999 at the same time, nor does 9*.9999 = 9


Looks like a typo. -x = -0.99999... This allows you to subtract out the infinite repeating part in step 4.

As to the 9*.99999= 9, well that's just one of the little enjoyments of considering infinitesimals. I think the easiest way to grasp it is to realize that last0.00000....09 doesn't really exist because that final 0..0001 is for all intents and purposes equal to zero (I'm common sensing, this is not the correct answer). 

I also think a lot of ambiguity goes away if instead of saying 0.99999.. I say 1/9, and I don't think anybody questions whether 1/9*9 = 1.


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