**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**!

Started by
qwerty841
, Aug 24 2004 10:15 PM

326 replies to this topic

Posted 26 August 2004 - 04:07 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**!

Posted 26 August 2004 - 04:16 PM

talking about the limit of a number is "stupid", unuseful (the limit of a number is the number itself )

.9999.... is the limit of the seria 0.9 0.09 0.009 0.0009 ..., the limit = 1 so .999.... = 1

.9999.... is the limit of the seria 0.9 0.09 0.009 0.0009 ..., the limit = 1 so .999.... = 1

Posted 26 August 2004 - 06:40 PM

it still doesnt make sense to me...

Posted 26 August 2004 - 06:47 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

so as the limite is 1, 0.9999...=1

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

Posted 26 August 2004 - 06:52 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

Posted 26 August 2004 - 07:11 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...)

Posted 26 August 2004 - 08:19 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 ).

Posted 26 August 2004 - 09:53 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

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

Posted 27 August 2004 - 01:37 AM

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

Posted 27 August 2004 - 02:15 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.

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

Posted 27 August 2004 - 09:17 AM

This is absolute nonsense(and logic by definition cannot be wrong, though it might not really be logic)

There are many things you can find "logical" but that are completely wrong (like the words you just said )

Posted 27 August 2004 - 02:35 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)

Posted 28 August 2004 - 05:20 AM

i really started something

Posted 28 August 2004 - 09:03 AM

it happens from time to time

Posted 28 August 2004 - 09:20 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 ...

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 ...

Posted 28 August 2004 - 09:30 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

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

Posted 28 August 2004 - 11:18 AM

sorry that I have not expressed myself correctly but I'm not to fond of

english math terms

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.

english math terms

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.

Posted 28 August 2004 - 04:31 PM

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

Posted 28 August 2004 - 04:37 PM

You can, when time == infinite This "infinite" thing is the key of everything, and that's why we can see that 0.999... = 1 because there is anYou can always say that the lim to x -> inf. is 0 but you can NEVER say

that y will be 0 at any time.

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

Posted 29 August 2004 - 01:40 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).

Posted 30 August 2004 - 10:01 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.

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.

Posted 30 August 2004 - 10:33 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

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

Posted 30 August 2004 - 10:44 PM

I think like OVERLORD.

Posted 31 August 2004 - 04:49 AM

and I think like ROOKIE and Crimson

Posted 31 August 2004 - 08:24 AM

We never spoke about calculators in this topic... there is no question about floating point precision here0.999(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.

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

We have a word in french to characterize the real numbers: we say their group is "

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! ), that's because 0.999... and 1 are

ok for "two diffrent numbers cannot equal each other" .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).

but who said they were unequals?

Posted 31 August 2004 - 08:37 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

But the conclusion is the same

Posted 31 August 2004 - 10:56 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

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

Posted 31 August 2004 - 12:09 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

You can't have numbers with a first & a last chiffre, with infinite chiffres between them

Posted 31 August 2004 - 12:19 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.

Posted 31 August 2004 - 12:36 PM

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

Posted 31 August 2004 - 12:45 PM

pi has an infinite number of decimals !

Posted 31 August 2004 - 12:46 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 ...

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 ...

Posted 31 August 2004 - 01:00 PM

ok, how about this:

to use your rule-

1> .5*(.999oo)+(.999oo) > .999oo

to use your rule-

1> .5*(.999oo)+(.999oo) > .999oo

Posted 31 August 2004 - 01:12 PM

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

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

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

Posted 31 August 2004 - 02:03 PM

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

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

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

Posted 31 August 2004 - 02:42 PM

again, im not a math person but i think you get what im trying to say..5*(.999oo)+(.999oo) < 1? are you sure about that?

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

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

Posted 31 August 2004 - 03:15 PM

5*(.999oo)+(.999oo) < 1

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

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

Posted 31 August 2004 - 03:18 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

2nd)

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

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

2nd)

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

Posted 31 August 2004 - 03:40 PM

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

Posted 31 August 2004 - 03:53 PM

that makes absolutely no sense to me....5*(.99999... + .99999...) = .5*2*(.99999...) = .99999... but is not > .99999... :s as it's the same number

@huhn: sometimes ignorance is the catalyst of innovation

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