Is 1 = 0.9999......

[TuxDave]

Originally posted by: Kyteland
Wow, I had no idea that this would spark such a huge flame, I mean debate.

Just as an update the three mathematicians here at work (two with their phd) managed to convince all of the computer programmer types that 0.999... was indeed the same as 1. Whether you want to believe it or not, we converted all of the skeptics here. My mission is complete.

Yay! Go you! Now finish up convincing the 100+ ppl who voted no... lol

 

[SilentRunning]

Originally posted by: TuxDave

Originally posted by: Kyteland
Wow, I had no idea that this would spark such a huge flame, I mean debate.

Just as an update the three mathematicians here at work (two with their phd) managed to convince all of the computer programmer types that 0.999... was indeed the same as 1. Whether you want to believe it or not, we converted all of the skeptics here. My mission is complete.

Yay! Go you! Now finish up convincing the 100+ ppl who voted no... lol

Ain't gonna happen.

 

[bleeb]

PhD's also make mistakes. =)

 

[silverpig]

Originally posted by: Viper GTS

Originally posted by: spyordie007

Originally posted by: spidey07
bleep,

you can believe what you want.

But there really isn't any debate to this.

They are the same number. Just as 1 + 1 = 2. (or 1.999...)

What Spidey said, I cant believe that so many people voted No, it just proves the lack of real technical or mathematical skills of ATOTers. Maybe if I rephrase it (again) it will help some of you understand...

.9999999........ is infinitely close to 1, it is not an approximation at all it is infinitely close. For you to be able to say that it is = ~1 would assume that it terminates eventually and if it terminates eventually it is ?? 1 however if it does not terminate ever .99999?c.. = 1

There?fs nothing to debate here for scientists, mathematicians and engineers alike, .999?c.. is equal to 1

-Spy

He speaks the truth. Many of you seem to have trouble wrapping your minds around the concept of a repeating, non-ending number like 0.999...

I too had trouble with the concept, & argued for quite some time with my dad when he presented the idea to me.

I believe I was 10 at the time.

Viper GTS

Haha.

 

[MadRat]

Originally posted by: RossGr

x = 0.999...
10x= 9.999...
10x - x =9.999... - 0.999...
9x = 9

this algebraic manipulation, is not a proof, it is a demonstration. Just because this trick does not constitute a formal proof does not mean the end result is not correct. It is, .999.... =1

....I do not buy the philosophical BS. Luvly, your are simply blowing hot air. A Philosopher can talk all they want about their concept of unity it simply does not apply, here we are talking about the real number system, if you want the correct result, you MUST talk to a mathematician, after all, who do you suppose built the real number system?

If .999... can exist then so can a difference between 1 and that number. The problem is that the same people that insist that .999... does exist are the same ones that say it can be represented. Unfortunately .999... cannot be represented on the number line meaning then it doesn't exist. At the same time if you accept that .999... does exist then there must be a difference between 1 and that number. To say that they are the same is a copout because to define .999... as anything but 1 means a difference exists. By the definition of .999... it does not equal 1 and therefore there must be a difference bewteen them. Since you claim that no difference exists (because you say that .999...=1) then it also means the .999... value also does not exist. Philosophically and by your own rules .999... either realistically neither does exist or they ideally (being .999... and the difference of 1-.999...) both exist, therefore its a pointless argument. The argument leaves mathematics and becomes one of philosophy.

You cannot have it both ways.

 

[ElFenix]

Originally posted by: MadRat

Originally posted by: RossGr

x = 0.999...
10x= 9.999...
10x - x =9.999... - 0.999...
9x = 9

this algebraic manipulation, is not a proof, it is a demonstration. Just because this trick does not constitute a formal proof does not mean the end result is not correct. It is, .999.... =1

....I do not buy the philosophical BS. Luvly, your are simply blowing hot air. A Philosopher can talk all they want about their concept of unity it simply does not apply, here we are talking about the real number system, if you want the correct result, you MUST talk to a mathematician, after all, who do you suppose built the real number system?

If .999... can exist then so can a difference between 1 and that number. The problem is that the same people that insist that .999... does exist are the same ones that say it can be represented. Unfortunately .999... cannot be represented on the number line meaning then it doesn't exist. At the same time if you accept that .999... does exist then there must be a difference between 1 and that number. To say that they are the same is a copout because to define .999... as anything but 1 means a difference exists. By the definition of .999... it does not equal 1 and therefore there must be a difference bewteen them. Since you claim that no difference exists (because you say that .999...=1) then it also means the .999... value also does not exist. Philosophically and by your own rules .999... either realistically neither does exist or they ideally (being .999... and the difference of 1-.999...) both exist, therefore its a pointless argument. The argument leaves mathematics and becomes one of philosophy.

You cannot have it both ways.

no... no, there can't be another number between .999... repeated infitnitely and 1, because its the same number!

just because the string of 0s is infinite when you subtract .999... from 1 doesn't make it anything more than 0.

 

[spyordie007]

Originally posted by: bleeb
SO HAS THE ISSUE BEEN RESOLVED WITHOUT A DOUBT??? =)

yes, and it was long before this thread ever came into existance.

In the rules of mathmatics ".99999...." is exactly the same thing as "1", we could easily talk about other ideas and theories where we are unsure as to whether the number "1" exists all day however based upon the rules of mathmatics the answer is simply a resounding "yes".

If you want to startup your own theorm of mathmatics I eagerly await the book (it should be quite interesting to see the similarities and differances between the currently accepted rules of mathmatics) however my answer of "yes" is based upon the currently world-wide accepted rules of mathmatics, both what I learned in calculus and in "real life".

-Spy

 

[TuxDave]

Originally posted by: MadRat


By the definition of .999... it does not equal 1 and therefore there must be a difference bewteen them.
You cannot have it both ways.

eh.... I disagree...

 

[Viper GTS]

You need to understand limits for this...

Viper GTS

 

[spyordie007]

By the definition of .999... it does not equal 1 and therefore there must be a difference bewteen them.
You cannot have it both ways.

You are right in that you cannot have it both ways, the problem is that you believe the definition of .999.... does not equal 1 which leads me to believe that you never got into higher level math.

It's not that I want to make this any more of a "flame war" but this is going to be a hard concept for those who have never worked in higher math, particularly calculus where the concept of limits is introduced. In fact the most conclusive proof that 1 = 0.9999...... is lim x -> infinity of 1-1x10^-x so please don?t take it personally if some people get aggravated when you tell them otherwise. If someone came up to you and told you that you were wrong about something you knew to be absolutely true you would also feel a little threatened. I don?t want to say that you are "dumb" but please accept that there are people here with a higher level of math skills and they have conclusive proof that 1 = 0.9999......

-Spy

EDIT: view ViperGTS's post above mine for a much better representation of the "limits" equation proving that the answer is still "yes".

 

[NovaTone]

even if you haven't taken calculus, i made an earlier post that clearly shows 0.999... = 1 using high school algebra concepts...namely, using geometric series.

 

[spyordie007]

Originally posted by: NovaTone
even if you haven't taken calculus, i made an earlier post that clearly shows 0.999... = 1 using high school algebra concepts...namely, using geometric series.

Of course, and there is always the 3(1/3)=3*.3333...=.9999....=1 equasion that shows it with simple fractions. I was just saying that the concept becomes much easier to under stand as you begin to understand concepts such as limits (as you learn limits it is easier to understand why 1/3 is exactly equal to .333.... and that .999.... is exactly equal to 1).

-Spy

 

[MadRat]

Originally posted by: spyordie007

Originally posted by: NovaTone
even if you haven't taken calculus, i made an earlier post that clearly shows 0.999... = 1 using high school algebra concepts...namely, using geometric series.

Of course, and there is always the 3(1/3)=3*.3333...=.9999....=1 equasion that shows it with simple fractions. I was just saying that the concept becomes much easier to under stand as you begin to understand concepts such as limits (as you learn limits it is easier to understand why 1/3 is exactly equal to .333.... and that .999.... is exactly equal to 1).

-Spy

No, you ignore logic to make your equations work. If you take any number and times it by a product of two you'll end up with an even result. You've only shown how to make .333... into 1/3 with hocus pocus of using a limit as the definition of the product to gain an even numbered product, which cannot happen. You cannot add three equal values to define an even product because that product does not exist; every product of 3 will equal an odd numbered result.

The answer lies before the limit, not at the limit. The limit lay outside your product by definition. Its the arrogance of this whole argument that the limit=product that is absurd. If .999... can exist then a number can exist between 1 and it. Since it cannot by your definition of the limit then that means neither exists. If you insist that .999... does exist then you have to accept the difference between 1 and .999... is possible, too.

You cannot have it both ways.

 

[spyordie007]

madhat-

If they were terminating decimals you would be correct in assuming that their product would end with an odd number. Once more you would also be correct in that there could be something "between" ".999...." and "1". However .999... is not a terminating decimal and therefore cannot be treated as such.

The problem is that you are missing an important part in your understanding of the underlying concept and simply assuming that because something is true for ".999" and ".99999999" that it is true of ".999...". I'm not trying to get you to change your mind, I'm simply asking that you keep your mind open because some of these concepts are hard to understand. You cannot use newtonian physics to define relitivity, you have to learn a new set of rules otherwise it simply does not "work".

-Spy

 

[Viper GTS]

Originally posted by: MadRat

Originally posted by: spyordie007

Originally posted by: NovaTone
even if you haven't taken calculus, i made an earlier post that clearly shows 0.999... = 1 using high school algebra concepts...namely, using geometric series.

Of course, and there is always the 3(1/3)=3*.3333...=.9999....=1 equasion that shows it with simple fractions. I was just saying that the concept becomes much easier to under stand as you begin to understand concepts such as limits (as you learn limits it is easier to understand why 1/3 is exactly equal to .333.... and that .999.... is exactly equal to 1).

-Spy

No, you ignore logic to make your equations work. If you take any number and times it by a product of two you'll end up with an even result. You've only shown how to make .333... into 1/3 with hocus pocus of using a limit as the definition of the product to gain an even numbered product, which cannot happen. You cannot add three equal values to define an even product because that product does not exist; every product of 3 will equal an odd numbered result.

The answer lies before the limit, not at the limit. The limit lay outside your product by definition. Its the arrogance of this whole argument that the limit=product that is absurd. If .999... can exist then a number can exist between 1 and it. Since it cannot by your definition of the limit then that means neither exists. If you insist that .999... does exist then you have to accept the difference between 1 and .999... is possible, too.

You cannot have it both ways.

You (and many others in this thread) are having trouble with the concept of an infinitely repeating decimal.

Yes, if you stop at ANY point before infinity you end up with something less than one. Conventional math cannot deal with this, you'll sit there for eternity watching the 9's go by waiting for your chance to evaluate it.

However, you have been given the tools to deal with such a problem (namely limits, infinite sums, etc.).

If you are not familiar with the use of such tools, don't assume those who know them are wrong.

Viper GTS

 

[MadRat]

Actually I'm not confused one bit. You have yet to define your answer within sound mathematical principles. You've only manipulated half truths to form an opinion and relabelled it as definitive. The truth lies outside human logic therefore you cannot prove your point.

 

[Viper GTS]

Originally posted by: MadRat
Actually I'm not confused one bit. You have yet to define your answer within sound mathematical principles. You've only manipulated half truths to form an opinion and relabelled it as definitive. The truth lies outside human logic therefore you cannot prove your point.

Out of curiousity, how old are you?

What level of math have you taken?

Viper GTS

 

[MadRat]

LOL.

Deflection from the main point of the argument is a form of concession. Viper, have you given up?

 

[SilentRunning]

Originally posted by: Viper GTS
You need to understand limits for this...

Viper GTS

Yep, that someone is you.


lim [1- 10(-n)] as n --> inf

does not equal

[1 - 10(-n)] as n --> inf

 

[Darien]

Originally posted by: MadRat
LOL.

Deflection from the main point of the argument is a form of concession. Viper, have you given up?

When I was reading your argument as to why .999...!= 1, I was wondering what level of math you've taken as well.



So care to answer?

 

[Viper GTS]

Originally posted by: MadRat
LOL.

Deflection from the main point of the argument is a form of concession. Viper, have you given up?

I seriously want to know, you can PM it to me if you'd rather not post it.

It has nothing to do with the argument, which you have only "won" by refusing relatively simple math.

Viper GTS

 

[Darien]

Q: How many mathematicians does it take to convince computer programmer types that 0.999... was indeed the same as 1 at Kyteland's workplace?


A: Three, but two of them must have PHD's and ignore that fact that wasn't the question that was asked.

You need to understand numbers to realize that .9999... = 1

 

[SilentRunning]

Originally posted by: Darien

Q: How many mathematicians does it take to convince computer programmer types that 0.999... was indeed the same as 1 at Kyteland's workplace?


A: Three, but two of them must have PHD's and ignore that fact that wasn't the question that was asked.

You need to understand numbers to realize that .9999... = 1

Why are you replying to my tag line? Can't you read?

 

[MadRat]

My age and training are irrelevant. The arguments you have were unsound and I have yet to question your age because its irrelevant. If you are insecure about the reasons behind the answer you cite then perhaps you shouldn't be in the argument in the first place. I'm am quite content that my argument is on solid ground and cannot be disproven.

Numbers follow constant laws. The argument for .333...=1/3, Viper, does not follow the constant that any product of 3 will equate to an odd number. The argument that .999...=1 also does not follow sound mathematical constants, therefore it must not be true. There is an equal likelihood that either the .999... does or does not exist, both arguments in which case neither would be equal to 1 by definition.

 

[RossGr]

Ahh.... Leave it to Mudrat to claim falsehood of basic mathematics with totally unsubstanticated claims, it is obvious to him, therefore it is god given fact. To Matrat ignorance is the final and end all argument.

What do you mean I want it both ways? There is only one possible way. Since I can concieve of .99... exitsting, it exists, seems that ought to be right down your ally, being philosophical and all. It has a fixed postion on the real number line which corresponds to the postion occupied by 1. Sorry if you do not like the fact that we have several representations for the same point on the number line, this is just a basic fact. All rational numbers have multilple representations. A rational number is any number which can be represented as a ratio of 2 integers, these numbers are charaterised by having either a terminating decimal representation like 1/2 = .5 or a infinitly repeating pattern like 1/3 = .33.... . By this definition .99... qualifies as the decimal representation of a rational number, that number is 1.

Matrat being a selfstyled philosopher (his calims, I have seen nothing of substance from him ) seems to feel that since no qualifcations are necessary to be a philosopher the same is true in all fields and that he is uniquely qualified to have final judgement because he has no qualifactions.

This simply is not the way it works, the real number line is man made. Real numbers exist only as tool invented by man, the men who invented and construted this tool were mathematicians, this is our toy and we know how it works. The only valid mathematical statement Matrat is capable of is "I DO NOT KNOW" , I surely would like to hear him say it.