Why is 0 11111 9 0 999999

1 = 0.9 ... (period)?!?!

Hello,



I have the following problem:



I firmly believe that 1 is not the same as 0.999 ... (periodically)

1=0.9999...

I mean, no matter how many nines there are after the decimal point, there will ALWAYS be a small part, no matter how small, so that it is exactly one!



If so, it should be like this: (even if I know that in principle there is no such number) -> 1 = 0.99 ... + 0.0 ... 1



I would be very interested in what you others think of it :-)
Suitable for OnlineMathe:

Online exercises (exercises) at unterricht.de:

DK2ZA

9:16 p.m., February 12, 2008

It is 0.999999 ..... = 1

 

Proof:

 

1/9 = 0,1111111.......

 

2/9 = 0,2222222......

 

etc. to

 

9/9 = 0,99999999......

 

But since 9/9 = 1

 

is

 

0,9999999.....   =  1

 

 

 

GREETING, DK2ZA

 

anonymous

9:22 pm, February 12th, 2008

Your reasoning is sound for every finite decimal fraction of the form 0.99 .... 9 |

But not for the periodic decimal fraction, which has an INFINITE number of digits. Proof of contradiction, if you do not like the argument of your colleague: Assuming you are right, the difference is> 0. Then there is a number that is really between 0.99999 ... and 1. So note: it really has to be bigger than 0.99999 ...! Just give them up and I'll throw in the towel.
Hello,

First of all thanks for the fast answers! :-)

Unfortunately I didn't have time to answer yesterday.



@Your reasoning is valid for every finite decimal fraction of the form 0.99 .... 9 |

But not for the periodic decimal fraction, which has an INFINITE number of digits. Proof of contradiction, if you do not like the argument of your colleague: Assuming you are right, the difference is> 0. Then there is a number that is really between 0.99999 ... and 1. So note: it really has to be bigger than 0.99999 ...! Just give them up and I'll throw in the towel.



Of course there is a number that is greater than 0.99999 ... or 0.999999 ... and that is in turn less than 0.9999999 ...



It just can't be that you can say that a finite number (1) is exactly the same as an infinite number (0.99 ...). I mean it is clear that the difference is so extra small or infinitely small that you can simply leave it out, calculate with it and get the right result. But it can never be exactly the same.

Somehow there is a limit to how long the text can be.



If you look at a number line you can see that the number 0.99 .. can never meet the number 1 or you simply cannot enter the number 0.99 .. precisely because it never ends.
this very small part is called "h" ... so 0.9999 ... = 1- h
@ This very small part is called "h" ... so 0.9999 ... = 1- h



Yeah, there is someone who knows his way around! :-) (* wink *)



That's exactly what I meant by 1 = 0.9 .. + 0.0..1 (in my first picture).



@Needhelp: Is there any proof of what you said / wrote? Would be really great.

@ Dk2ZA

Why is 9/9 = 0.99999 that's 1 or I'm stupid?!?!?!

@ Why is 9/9 = 0.99999 that's 1 or I'm stupid?!?!?!



Yeah, that's supposed to be the proof that 1 = 0.99 .. is ^^

Yes but 9/9 is not 0.999999

anonymous

6:03 p.m., 02/13/2008





Of course there is a number that is greater than 0.99999 ... or 0.999999 ... and that is in turn less than 0.9999999 ...


Tach, math pipe, but haven't really thought about it: we're talking about 0, period 9, right? The number with the infinitely many 9s at the back? It doesn't get longer if you insert a 9, that's the really great joke about infinity.







Of course there is a number that is greater than 0.99999 ... or 0.999999 ... and that is in turn less than 0.9999999 ...


Tach, math pipe, but haven't really thought about it: we're talking about 0, period 9, right? The number with the infinitely many 9s at the back? It doesn't get longer if you insert a 9, that's the really great joke about infinity.


Yeah, that's right.
So that's actually very easy if you are familiar with fractions.
So 0.3 (period)
0.6 (period)
0.9 (period)
so we have already come to the 0.9 (period), and we see that it is too.
and if a fraction has the same number twice below and above the fraction line, it is a whole
so 0.9 (period)

hope I could help
So I guess that your post will no longer interest the thread creator after 3 years (and two days). ;-)
This question was automatically closed because the questioner was no longer interested in the question.