Jump to content



Photo
- - - - -

.999999999999... = 1 ?


  • This topic is locked This topic is locked
326 replies to this topic

#41 octobclrnts

octobclrnts

    Casio Freak

  • Members
  • PipPipPipPip
  • 145 posts
  • Location:Pennsylvania, United States
  • Interests:Computers<br />Programming languages<br />Artificial Intelligence<br />Music (clarinet)

  • Calculators:
    Casio CFX 9850GB Plus
    Ti-89 Titanium

Posted 26 August 2004 - 05:07 PM

All the mathematical demonstrations given have simply proven that the limit of .999999... is 1. None of them have proven that .99999... itself is 1. A limit is the number that is approached but never reached!

#42 Overlord

Overlord

    Casio Technician

  • Moderator
  • PipPipPipPipPipPip
  • 355 posts
  • Gender:Male
  • Location:Brussels - Belgium
  • Interests:Math Researcher

  • Calculators:
    My head - C300 OS 3.00 - G100 Rom 1.02 - G65 - G60 - G25

Posted 26 August 2004 - 05:16 PM

talking about the limit of a number is "stupid", unuseful (the limit of a number is the number itself :P)
.9999.... is the limit of the seria 0.9 0.09 0.009 0.0009 ..., the limit = 1 so .999.... = 1

#43 CrimsonCasio

CrimsonCasio

    UCF Ambassador

  • [Legends]
  • PipPipPipPipPipPipPipPipPipPip
  • 3579 posts
  • Gender:Male
  • Location:USA
  • Interests:Claculators, Stephen King, Video Games, Calculators, Programming, Calculators, Reading, Calculators... hmm, what else... Ah! Calculators!

  • Calculators:
    Algebra FX2.0, CFX 9850Ga+, Classpad 300

Posted 26 August 2004 - 07:40 PM

it still doesnt make sense to me... :(

#44 Bija

Bija

    Casio Fan

  • Members
  • PipPip
  • 44 posts

  • Calculators:
    Graph 25, Graph 100+ 1.05

Posted 26 August 2004 - 07:47 PM

0.99999999... is a limite not a defined number
so as the limite is 1, 0.9999...=1

it is infinitely close to 1,always more closer, the 'most' closer is 1

#45 CrimsonCasio

CrimsonCasio

    UCF Ambassador

  • [Legends]
  • PipPipPipPipPipPipPipPipPipPip
  • 3579 posts
  • Gender:Male
  • Location:USA
  • Interests:Claculators, Stephen King, Video Games, Calculators, Programming, Calculators, Reading, Calculators... hmm, what else... Ah! Calculators!

  • Calculators:
    Algebra FX2.0, CFX 9850Ga+, Classpad 300

Posted 26 August 2004 - 07:52 PM

by that I take it that your saying that .99999~ is not equal to 1, but infinately close to 1. that I could understand and agree with but I dont see how .9999~ = 1

#46 Orwell

Orwell

    Casio Overlord

  • Members
  • PipPipPipPipPipPipPip
  • 777 posts
  • Gender:Male
  • Location:Paris - France

  • Calculators:
    Casio AFX 1.02 / Casio ClassPad 300

Posted 26 August 2004 - 08:11 PM

0.99999... is the limit of the sequence 0, 0.9, 0.99, 0.999, 0.9999,... and this limit is also equal to 1. (Think at the example of the ball that someone drop against a wall: it first does 90% of the distance, then 99%, then 99,9% etc then finally hit the wall, so it finally does 100% of the way...)

#47 betoe

betoe

    UCF Spanish Translator

  • Admin
  • PipPipPipPipPipPipPip
  • 846 posts
  • Gender:Male
  • Location:Guadalajara/Mazatlan, Mexico.
  • Interests:Electronics, SW development, automotive. Swim->bike->run

  • Calculators:
    Algebra FX2.0 (R.I.P.), Classpad 300

Posted 26 August 2004 - 09:19 PM

On an university exam, if you have the 3.9999 result, put 4 and look what your teacher will think (here in my uny its bad :D).

#48 Overlord

Overlord

    Casio Technician

  • Moderator
  • PipPipPipPipPipPip
  • 355 posts
  • Gender:Male
  • Location:Brussels - Belgium
  • Interests:Math Researcher

  • Calculators:
    My head - C300 OS 3.00 - G100 Rom 1.02 - G65 - G60 - G25

Posted 26 August 2004 - 10:53 PM

if you have 3.9999 don't put 4, it's bad for teachers that like precision.
if you have 3.9999..., you can put 4, and if your teacher says it's wrong just tell him to consult a real math teacher :P

#49 2072

2072

    Casio over god

  • Admin
  • PipPipPipPipPipPipPipPip
  • 1550 posts
  • Gender:Male
  • Location:Somewherebourg
  • Interests:Cinema, Programming, Music and a lot of thing...

  • Calculators:
    AFX2 ROM 1.02, CFX-9940GT+, FX-180P-Plus

Posted 27 August 2004 - 02:37 AM

The fact that 0.9999...=1 is a mathematical fact not a "logical" fact. Logical != mathematical

#50 CrimsonCasio

CrimsonCasio

    UCF Ambassador

  • [Legends]
  • PipPipPipPipPipPipPipPipPipPip
  • 3579 posts
  • Gender:Male
  • Location:USA
  • Interests:Claculators, Stephen King, Video Games, Calculators, Programming, Calculators, Reading, Calculators... hmm, what else... Ah! Calculators!

  • Calculators:
    Algebra FX2.0, CFX 9850Ga+, Classpad 300

Posted 27 August 2004 - 03:15 AM

logic and math should be equal, else one of them is wrong. (and logic by definition cannot be wrong, though it might not really be logic)

therefor it should be possible to explain this in logical terms.

#51 Orwell

Orwell

    Casio Overlord

  • Members
  • PipPipPipPipPipPipPip
  • 777 posts
  • Gender:Male
  • Location:Paris - France

  • Calculators:
    Casio AFX 1.02 / Casio ClassPad 300

Posted 27 August 2004 - 10:17 AM

(and logic by definition cannot be wrong, though it might not really be logic)

This is absolute nonsense :blink:
There are many things you can find "logical" but that are completely wrong (like the words you just said :) )

#52 CrimsonCasio

CrimsonCasio

    UCF Ambassador

  • [Legends]
  • PipPipPipPipPipPipPipPipPipPip
  • 3579 posts
  • Gender:Male
  • Location:USA
  • Interests:Claculators, Stephen King, Video Games, Calculators, Programming, Calculators, Reading, Calculators... hmm, what else... Ah! Calculators!

  • Calculators:
    Algebra FX2.0, CFX 9850Ga+, Classpad 300

Posted 27 August 2004 - 03:35 PM

i dont want this to become a debate of the definetion of logic, but: what im saying is that any statement that is logical must in fact also be true, otherwise it is not really logic (though it may be based on logical thinking)

#53 qwerty841

qwerty841

    Casio Freak

  • Members
  • PipPipPipPip
  • 198 posts
  • Gender:Male
  • Location:vernal

  • Calculators:
    ClassPad 300,TI 83 PSE,TI Voyage 200,Windows Calculator

Posted 28 August 2004 - 06:20 AM

i really started something :)

#54 CrimsonCasio

CrimsonCasio

    UCF Ambassador

  • [Legends]
  • PipPipPipPipPipPipPipPipPipPip
  • 3579 posts
  • Gender:Male
  • Location:USA
  • Interests:Claculators, Stephen King, Video Games, Calculators, Programming, Calculators, Reading, Calculators... hmm, what else... Ah! Calculators!

  • Calculators:
    Algebra FX2.0, CFX 9850Ga+, Classpad 300

Posted 28 August 2004 - 10:03 AM

it happens from time to time ;)

#55 huhn_m

huhn_m

    Casio Maniac

  • Admin
  • PipPipPipPipPipPipPipPip
  • 1957 posts
  • Gender:Male
  • Location:Germany / Dresden
  • Interests:Assembler(!!!)
    Computers and Programming
    Operating Systems
    Programmable Calculators
    Maths and everything arround it

  • Calculators:
    FX-82SX / AFX 2.0+ (ROM 1.03) / FX 1.0+ (ROM 1.03)

Posted 28 August 2004 - 10:20 AM

some said it really well ...

0.9999... approaches 1 but NEVER actually gets it. it gets closer and closer.

It's like a parable that approaches the x axis but never intersects it.

You can't say "of course it touches the axis because sometimes it gets 0
thats nonsens. Write for such a function in a test that it touches the x axis and
you'll fail the question thats how simply it is.

And if math isn't anymore logic so why to believe in math ...

#56 Bija

Bija

    Casio Fan

  • Members
  • PipPip
  • 44 posts

  • Calculators:
    Graph 25, Graph 100+ 1.05

Posted 28 August 2004 - 10:30 AM

a parable never intersects the x axis but the limit when x tends towards infinite IS 0 !!

as the same considering the following series :
un=(10^n-1)/(10^n)=1-1/(10^n)

it is clear that the limite of that series is 0.9999...
but as 1/(10^n) tends towards 0, the limite is also 1

it is perfectly logic to me

#57 huhn_m

huhn_m

    Casio Maniac

  • Admin
  • PipPipPipPipPipPipPipPip
  • 1957 posts
  • Gender:Male
  • Location:Germany / Dresden
  • Interests:Assembler(!!!)
    Computers and Programming
    Operating Systems
    Programmable Calculators
    Maths and everything arround it

  • Calculators:
    FX-82SX / AFX 2.0+ (ROM 1.03) / FX 1.0+ (ROM 1.03)

Posted 28 August 2004 - 12:18 PM

sorry that I have not expressed myself correctly but I'm not to fond of
english math terms :D

anyways I meant that there are graphs that approach the x axis but NEVER
intersect / touch it. Thats the same with this.

You can always say that the lim to x -> inf. is 0 but you can NEVER say
that y will be 0 at any time.

take 1/(sqrt(x)).
My math teacher would kill me if I said it would be 0 at any time.
Do you now understand what I mean.
You can not say that the limes is the same as the equal sign.

#58 CrimsonCasio

CrimsonCasio

    UCF Ambassador

  • [Legends]
  • PipPipPipPipPipPipPipPipPipPip
  • 3579 posts
  • Gender:Male
  • Location:USA
  • Interests:Claculators, Stephen King, Video Games, Calculators, Programming, Calculators, Reading, Calculators... hmm, what else... Ah! Calculators!

  • Calculators:
    Algebra FX2.0, CFX 9850Ga+, Classpad 300

Posted 28 August 2004 - 05:31 PM

I agree with huhn, thats exactly what I was thinking.

#59 Orwell

Orwell

    Casio Overlord

  • Members
  • PipPipPipPipPipPipPip
  • 777 posts
  • Gender:Male
  • Location:Paris - France

  • Calculators:
    Casio AFX 1.02 / Casio ClassPad 300

Posted 28 August 2004 - 05:37 PM

You can always say that the lim to x -> inf. is 0 but you can NEVER say
that y will be 0 at any time.

You can, when time == infinite :D This "infinite" thing is the key of everything, and that's why we can see that 0.999... = 1 because there is an infinite number of 9 :lol:

To be more "complete" huhn, you are right when you say that 1/(sqrt(x)) will never be equal to 0, because when we study such functions we generally work with real numbers, and inf & -inf don't belong to this group, so there is no real value for x to have 1/(sqrt(x))==0 ;)

#60 CrimsonCasio

CrimsonCasio

    UCF Ambassador

  • [Legends]
  • PipPipPipPipPipPipPipPipPipPip
  • 3579 posts
  • Gender:Male
  • Location:USA
  • Interests:Claculators, Stephen King, Video Games, Calculators, Programming, Calculators, Reading, Calculators... hmm, what else... Ah! Calculators!

  • Calculators:
    Algebra FX2.0, CFX 9850Ga+, Classpad 300

Posted 29 August 2004 - 02:40 AM

that still doesnt work, .9999 approches 1 infitately but will never reach it. it cant by its very nature (two diffrent numbers cannot equal each other).

#61 R00KIE

R00KIE

    Casio Freak

  • Members
  • PipPipPipPip
  • 155 posts
  • Location:Portugal
  • Interests:Electronics, games, programming

  • Calculators:
    HP49G ROM 1.24; CASIO CFX-9850GB PLUS;CASIO FX-6300G; CASIO FX-82TL

Posted 30 August 2004 - 11:01 PM

0.999(9) WILL NEVER BE EQUAL TO 1
it's very simple, it's just like that.
the only reason that makes us say that 0.999(9) is equal to one is because the error of assuming that isn't important for the operation we do and it's a shorter number to represent and easier to work with.
Another thing that might some people to say that 0.999(9)=1 is because of the finite precision of calculators that after a some calculations that give results that put the floating point precision to test, the calculators mess thing up.

#62 Overlord

Overlord

    Casio Technician

  • Moderator
  • PipPipPipPipPipPip
  • 355 posts
  • Gender:Male
  • Location:Brussels - Belgium
  • Interests:Math Researcher

  • Calculators:
    My head - C300 OS 3.00 - G100 Rom 1.02 - G65 - G60 - G25

Posted 30 August 2004 - 11:33 PM

and this error is exactly equal to zero when you have an infinite number of '9' in your number, so 0.999... = 1, it's very simple lol :)

i think each part will have many difficulties to convince the other part... see, we've already written 62 posts :P

#63 Daruosh

Daruosh

    Casio Freak

  • Members
  • PipPipPipPip
  • 285 posts
  • Gender:Male
  • Location:Tehran - Iran
  • Interests:Computer Programming, Electronics, Image Processing, Neural Networks, AI, System Development, Calc, Guitar, Music,

  • Calculators:
    CP 300 OS 3.03, Algebra FX 2.0 Plus ROM 1.05, CG-20

Posted 30 August 2004 - 11:44 PM

I think like OVERLORD.

#64 huhn_m

huhn_m

    Casio Maniac

  • Admin
  • PipPipPipPipPipPipPipPip
  • 1957 posts
  • Gender:Male
  • Location:Germany / Dresden
  • Interests:Assembler(!!!)
    Computers and Programming
    Operating Systems
    Programmable Calculators
    Maths and everything arround it

  • Calculators:
    FX-82SX / AFX 2.0+ (ROM 1.03) / FX 1.0+ (ROM 1.03)

Posted 31 August 2004 - 05:49 AM

and I think like ROOKIE and Crimson :)

#65 Orwell

Orwell

    Casio Overlord

  • Members
  • PipPipPipPipPipPipPip
  • 777 posts
  • Gender:Male
  • Location:Paris - France

  • Calculators:
    Casio AFX 1.02 / Casio ClassPad 300

Posted 31 August 2004 - 09:24 AM

0.999(9) WILL NEVER BE EQUAL TO 1
Another thing that might some people to say that 0.999(9)=1 is because of the finite precision of calculators that after a some calculations that give results that put the floating point precision to test, the calculators mess thing up.

<{POST_SNAPBACK}>

We never spoke about calculators in this topic... there is no question about floating point precision here :)

I have another argument (and for me, you can't refuse it, unless you don't know what the real numbers are :rolleyes: )

We have a word in french to characterize the real numbers: we say their group is "dense". That means that between 2 differents real numbers (let's say A and B ), there is allways a third one C between A and B, strictly different from them. (For all A,B reals, there is C real in such a way that A < C < B is verified.)
If you choose 0.001 and 0.002, there is 0.0015 betwen them; between 10^-20 and 2*10^-20, there is 1.5*10^-20 etc...

If you postulate that 0.999... and 1 are two different numbers, then you should be able to find another different number between them, and different from them. But you cannot find a number x in such a way that 0.999999... < x < 1, because of the infinite number of the chiffre '9' :) This real x should be "closer to 1" than 0.9999... , however we all assumed here that 0.999... was infinitely close.

Thus, if you cannot find this number x (it can't be 0.999... with "more" '9' than 0.999... itself! :P ), that's because 0.999... and 1 are not two different real numbers. B)

that still doesnt work, .9999 approches 1 infitately but will never reach it. it cant by its very nature (two diffrent numbers cannot equal each other).

ok for "two diffrent numbers cannot equal each other" .
but who said they were unequals? ;)

#66 Orwell

Orwell

    Casio Overlord

  • Members
  • PipPipPipPipPipPipPip
  • 777 posts
  • Gender:Male
  • Location:Paris - France

  • Calculators:
    Casio AFX 1.02 / Casio ClassPad 300

Posted 31 August 2004 - 09:37 AM

I have to correct something in my last post above: the correct definition for the "density" of the real numbers is that between 2 different real numbers, there is allways a rationnal number different from them."
But the conclusion is the same :)

#67 huhn_m

huhn_m

    Casio Maniac

  • Admin
  • PipPipPipPipPipPipPipPip
  • 1957 posts
  • Gender:Male
  • Location:Germany / Dresden
  • Interests:Assembler(!!!)
    Computers and Programming
    Operating Systems
    Programmable Calculators
    Maths and everything arround it

  • Calculators:
    FX-82SX / AFX 2.0+ (ROM 1.03) / FX 1.0+ (ROM 1.03)

Posted 31 August 2004 - 11:56 AM

and so 0,0...1 is equal to zero?
and 1,0....1 is equal to one and so on ... I don't think this is a valid argument
since it fits for an endless amount of infinite numbers :)

#68 Orwell

Orwell

    Casio Overlord

  • Members
  • PipPipPipPipPipPipPip
  • 777 posts
  • Gender:Male
  • Location:Paris - France

  • Calculators:
    Casio AFX 1.02 / Casio ClassPad 300

Posted 31 August 2004 - 01:09 PM

No, because 0,000...01 and 1,000...01 are finite number (because they have 'a "last chiffre", here the '1', however 0,999... hasn't such a "last chiffre") :)
You can't have numbers with a first & a last chiffre, with infinite chiffres between them ;)

#69 CrimsonCasio

CrimsonCasio

    UCF Ambassador

  • [Legends]
  • PipPipPipPipPipPipPipPipPipPip
  • 3579 posts
  • Gender:Male
  • Location:USA
  • Interests:Claculators, Stephen King, Video Games, Calculators, Programming, Calculators, Reading, Calculators... hmm, what else... Ah! Calculators!

  • Calculators:
    Algebra FX2.0, CFX 9850Ga+, Classpad 300

Posted 31 August 2004 - 01:19 PM

correct me if im wrong, but I dont think that anything that has to do with infinity can be "real", therefor your rule wouldnt apply.

#70 Orwell

Orwell

    Casio Overlord

  • Members
  • PipPipPipPipPipPipPip
  • 777 posts
  • Gender:Male
  • Location:Paris - France

  • Calculators:
    Casio AFX 1.02 / Casio ClassPad 300

Posted 31 August 2004 - 01:36 PM

1/3 = 0.33333... has an infinite number of '3', and is naturally real like 0.9999... :hammer:

#71 Overlord

Overlord

    Casio Technician

  • Moderator
  • PipPipPipPipPipPip
  • 355 posts
  • Gender:Male
  • Location:Brussels - Belgium
  • Interests:Math Researcher

  • Calculators:
    My head - C300 OS 3.00 - G100 Rom 1.02 - G65 - G60 - G25

Posted 31 August 2004 - 01:45 PM

pi has an infinite number of decimals !

#72 huhn_m

huhn_m

    Casio Maniac

  • Admin
  • PipPipPipPipPipPipPipPip
  • 1957 posts
  • Gender:Male
  • Location:Germany / Dresden
  • Interests:Assembler(!!!)
    Computers and Programming
    Operating Systems
    Programmable Calculators
    Maths and everything arround it

  • Calculators:
    FX-82SX / AFX 2.0+ (ROM 1.03) / FX 1.0+ (ROM 1.03)

Posted 31 August 2004 - 01:46 PM

so what about 1.9999999... is this equal 2 too and all the other numbers ending with
this.

I'm still on the side that this is only true if you accept a loss of precission.
(see above). I don't know about THIS real number definition you mentioned so
I won't take it into account. I'll ask my physics teacher on thursday since she
really knows a lot ... maybe she can help ...

#73 CrimsonCasio

CrimsonCasio

    UCF Ambassador

  • [Legends]
  • PipPipPipPipPipPipPipPipPipPip
  • 3579 posts
  • Gender:Male
  • Location:USA
  • Interests:Claculators, Stephen King, Video Games, Calculators, Programming, Calculators, Reading, Calculators... hmm, what else... Ah! Calculators!

  • Calculators:
    Algebra FX2.0, CFX 9850Ga+, Classpad 300

Posted 31 August 2004 - 02:00 PM

ok, how about this:

to use your rule-
1> .5*(.999oo)+(.999oo) > .999oo

#74 Orwell

Orwell

    Casio Overlord

  • Members
  • PipPipPipPipPipPipPip
  • 777 posts
  • Gender:Male
  • Location:Paris - France

  • Calculators:
    Casio AFX 1.02 / Casio ClassPad 300

Posted 31 August 2004 - 02:12 PM

.5*(.999oo)+(.999oo) < 1? are you sure about that? :blink:

it is not a physics teacher we need, it's an algebra or analysys one :D

#75 Bija

Bija

    Casio Fan

  • Members
  • PipPip
  • 44 posts

  • Calculators:
    Graph 25, Graph 100+ 1.05

Posted 31 August 2004 - 03:03 PM

I've seen (with a maths teacher :-) in maths that 0.999999..=1

isn't that (and all the demonstrations we gave) enough ?

#76 CrimsonCasio

CrimsonCasio

    UCF Ambassador

  • [Legends]
  • PipPipPipPipPipPipPipPipPipPip
  • 3579 posts
  • Gender:Male
  • Location:USA
  • Interests:Claculators, Stephen King, Video Games, Calculators, Programming, Calculators, Reading, Calculators... hmm, what else... Ah! Calculators!

  • Calculators:
    Algebra FX2.0, CFX 9850Ga+, Classpad 300

Posted 31 August 2004 - 03:42 PM

.5*(.999oo)+(.999oo)  < 1? are you sure about that?  :blink:

it is not a physics teacher we need, it's an algebra or analysys one  :D

<{POST_SNAPBACK}>

again, im not a math person but i think you get what im trying to say.

and no, its not enough untill I here an explenation that makes sense.

#77 Overlord

Overlord

    Casio Technician

  • Moderator
  • PipPipPipPipPipPip
  • 355 posts
  • Gender:Male
  • Location:Brussels - Belgium
  • Interests:Math Researcher

  • Calculators:
    My head - C300 OS 3.00 - G100 Rom 1.02 - G65 - G60 - G25

Posted 31 August 2004 - 04:15 PM

5*(.999oo)+(.999oo)  < 1


.5*(.999oo) must be something like (.499oo) no ?

and (.499oo)+(.999oo) surely > 1

#78 huhn_m

huhn_m

    Casio Maniac

  • Admin
  • PipPipPipPipPipPipPipPip
  • 1957 posts
  • Gender:Male
  • Location:Germany / Dresden
  • Interests:Assembler(!!!)
    Computers and Programming
    Operating Systems
    Programmable Calculators
    Maths and everything arround it

  • Calculators:
    FX-82SX / AFX 2.0+ (ROM 1.03) / FX 1.0+ (ROM 1.03)

Posted 31 August 2004 - 04:18 PM

1)
I think what you ment was 0.5*((.99999...)+(.99999..))<1 because else it would be
approaching 1.5 ... but this way it approaches 1 again :) You
cracked their "logic" explanation :D

2nd)
she is a maths/algebra teacher too ... I only don't have her in my maths course ...

#79 Overlord

Overlord

    Casio Technician

  • Moderator
  • PipPipPipPipPipPip
  • 355 posts
  • Gender:Male
  • Location:Brussels - Belgium
  • Interests:Math Researcher

  • Calculators:
    My head - C300 OS 3.00 - G100 Rom 1.02 - G65 - G60 - G25

Posted 31 August 2004 - 04:40 PM

.5*(.99999... + .99999...) = .5*2*(.99999...) = .99999... but is not > .99999... :s as it's the same number

#80 CrimsonCasio

CrimsonCasio

    UCF Ambassador

  • [Legends]
  • PipPipPipPipPipPipPipPipPipPip
  • 3579 posts
  • Gender:Male
  • Location:USA
  • Interests:Claculators, Stephen King, Video Games, Calculators, Programming, Calculators, Reading, Calculators... hmm, what else... Ah! Calculators!

  • Calculators:
    Algebra FX2.0, CFX 9850Ga+, Classpad 300

Posted 31 August 2004 - 04:53 PM

.5*(.99999... + .99999...) = .5*2*(.99999...) = .99999... but is not > .99999... :s as it's the same number

<{POST_SNAPBACK}>

that makes absolutely no sense to me... :huh:

@huhn: sometimes ignorance is the catalyst of innovation ;)




1 user(s) are reading this topic

0 members, 1 guests, 0 anonymous users