Why does .99999999... = 1?

[RossGr]

<< its impossible, the reason you get that in the calculator is because of the flaw in the calculator. this is so simple all you need is common sense. >>



You need to take some math courses, this is not a result of a calculator....It is a result of Real Analysis.

Next time try reading some of the thread before posting, please!

 

[LaVoS]

Thats my point exactly... i think that our understanding of math is flawed... 3/3 = .99999999999999... not 1 so .333333333... is not the correct decimel for 1/3 and yes i am a HS Freshmen but that doesnt madder... 1= .99999999999999... and .9999999999... = 1 its that simple... there is no reason for it not to equal 1 because 3*3 = 9 and .33333... *3 = .99999... so umm yeah...

 

[Haircut]

Please, not again :frown:

 

[gqstyle09]

<< i am a HS Freshmen but that doesnt madder... >>


hehehe

 

[RSI]

It doesn't equal 1, math freaks just like to tell you that to screw with your mind.

-RSI

 

[SinNisTeR]

You need to take some math courses, this is not a result of a calculator....It is a result of Real Analysis.

Next time try reading some of the thread before posting, please!


Right.. you are some genius arent you?!


My new thread: does yes=no?

 

[DannyLove]

its called rounding up!

 

[spidey07]

this has been proven so many times,

read the thread in HT

 

[RossGr]

<< Right.. you are some genius arent you?! >>



LOL.... Therefore you must be the genius! LOL


Did you read any of the proofs presented, Or are you just a genius that knows these things without the disadvantage of having studied mathmatics?

 

[Harvey]

<< Why does .99999999... = 1? >>

Because nobody can dance in 3.99999996/4 time, and drummers have a hell of a time counting it out.

 

[SinNisTeR]

i never said i was a genius, it sounded that your derogative statement ment that you were smarter than me.

there is no need to see the proofs presented.. .9 != 1. its as simple as that. no matter how many 9s follow that.

.9999999999999999999999999 = .9999999999999999999999999 not 1.

 

[spidey07]

alright sinister, now you're just being an antagonist. read the HT thread, your self proclaimed delusions will hopefully disolve.

<edit> your != you're grammar edit

 

[ViperMagic]

if .999999999r = 1 then what does 1 - .00000000<infinite 0s>1 equal? .88888? But then that would equal .999r which equals 1!

 

[RossGr]

We went through this for a month on the HT fourm. Did you bother to read ANY of the posts in that thread?

I think not, obviously you are one of those who just know this sort of thing? Try reading and understanding the proofs. There is a field of study called Real Analysis which is presented in detail to Math Majors only. Do you have a university degee in Mathmatics? If you did this would not be a point to argue, it would simply be understood.

Think of it this way. For 2 numbers to be different there must be another number inbetween them, ie x-y=z. Now if

x =.99... and y =1 what is z considering that .99.... is an infinite string with NO END you cannot terminate it with a 1 or anything else because it goes on with out end. This is not a number which is growing or changing it is a fixed number .99... this is not a matter of rounding or approximation. This a fact of properly and carefully dealing with a number with an infinite tail of numerals.

A rational number is a number which can be represented by a fraction, every rational number has a decimal represention on the real number line. .33... is the decimal representation of the fraction 1/3. .99... is a decimal represention of 1.

It is to bad that the non-math types could not attempt to understand this concept rather then argue from faulty a priori knowledge.

 

[RossGr]

<< if .999999999r = 1 then what does 1 - .00000000<infinite 0s>1 equal? .88888? But then that would equal .999r which equals 1! >>



You cannot terminate an infinte string of digits with a number, if you teminate an infinte string it is no longer infinte. Just a very long string of digits. An infinite string of digits is just that , infinite. To say an infinite string follwed by something is speaking nonsense. You either have an infinte string or you don't!

 

[BigJohnKC]

I was thinking of what I thought could be a proof, but I came up with a fatal flaw in my thinking......in fact I think you, RossGr, posted these exact thoughts in that previous thread.....

it can be proven that there exists exactly one irrational number between consecutive rational numbers. Since .9999999999<infinite> and 1 are consecutive rational numbers it can be shown that there exists exactly one irrational number between these two numbers, so .9999999999<infinite> != 1...

But, as I was thinking this, I realized that I was trying to assume that .99999999<infinite> and 1 were consecutive rational numbers, and it is a fatal flaw in mathematics to assume the thing you are trying to prove....

I still don't think they are the same, but I have no mathematical reasoning behind that, just a feeling and thoughts about how the universe works....maybe I should have gotten my bachelor's in philosophy instead of mathematics...oh well, too late now. However, RossGr's proofs show somewhat conclusively that he is right. I still have yet to ask my graduate mathematics student friend the answer to this question....

 

[LaVoS]

If no one can prove that .9999999999... doesnt = 1 then i guess it does... hmmm

 

[BrintonAA]

Where did that really good thread about this in Highly Technical Forum go?

 

[RossGr]

This topic was beaten to death in HT forum a few weeks ago. I will not respond to posts to the HT thread. I will here. So if you wish to argue this do it here and please use a better argument then " it must be" or "it can't be". Please make an effort to read and understand some of the proofs that have been posted. If this is a tenant of your religion (1 =! .99....) then there is no point in discussing it. If you are indeed attempting to understand that this is a fact of the real number line and have some questions about the proofs then post away.

 

[LaVoS]

I know that .999999999999999999... does not relly equal 1 BUT accourding to Fractions and Decimles (and Algebra stuff and what not) it does... and what im trying to say is it is a flaw in our math system... why are we still usieng it if it is flawed? that .000000000000000000000000000000... (1) lil thing could affect something seriosuly that needs precice precision to build or do... you never know

 

[SinNisTeR]

LaVoS:

If no one can prove that .9999999999... doesnt = 1 then i guess it does... hmmm

I know that .999999999999999999... does not relly equal 1






You now have the answer... the end.

 

[NelsonMuntz]

I think the real problem here is not with the mathematical system we use, it works extremely well and I don't think it is going anywhere soon. The real problem is with the inability of our minds to really understand the depths of infinity. 0.999999 infinitely repeated does equal 1. It has been mathematically proven and some o those proofs have already been presented here. If you don't want to believe it, then that's fine, but you are snubbing your nose at the truth. If you really want to understand it, then you will need to search it out in whatever mathematical texts are available to you and hopefully you can find something about it. I first learned this from my 8th grade algebra teacher and have remembered the concept ever since (although I do not remember which particular proof he used to demonstrate it).

 

[thEnEuRoMancER]

I didn't read the previous posts so I'll just explain my understanding why 0.9999... = 1.

One can write 0.9999 as an infinite sum of 0.9 + 0.09 + 0.009 +.0009 + ...

Each next term is exactly one tenth of the previous one: 0.09 = 0.9/10, 0.009 = 0.09/10 and so on

A sum like this is called a sum of a geometric series (BTW: this topic is taught in high school in Europe, how about US?).
Each geometric series is defined with its first term a1 (in our case a1=0.9) and the ratio of two consecutive terms q (in our case q=1/10 = 0.1).

The sum of infinite series is calculated like this: S = a1*(1/(1-q))

So in our case: S = 0.9*(1/(1-0.1))=0.9*1/0.9 = 1

 

[juiio]

.9 repeating is 1. Thats it.

People that don't accept that just have problems believing that it could be true.

Accept that it is true, just like 1/3 is equal to .333repeating and 2/3 is equal to .666repeating. 3/3 is equal to .999repeating.

1 = 3/3 = .999repeating.

 

[LaVoS]

Thast not what i meant... i emant that .999999999... does not equal one because well does .9 look like 1? no it doenst... BUT mathmatically .9999999... DOES equal one... and i think this is weird... yep it is...