Is 1 = 0.9999......

[MaxFusion16]

Originally posted by: DrPizza

Originally posted by: MaxFusion16

Originally posted by: DrPizza
No way, YamahaXS, I've read the entire thread (not all at once, but catch up every time I see it)...

Let me pose this question for bleeb and any others who think they're correct that .999... != 1
would you be willing to wager $100 on it? (I'm willing to bet that .999repeating EQUALS EXACTLY 1)

To settle the bet, 1st we each put our $100 someplace where the loser can't renig. Then, we put the names of all accredited universities that have a math program in a hat (or narrow the choices to just U.S. universities to eliminate the language barrier... I'm not sure I'd know how to ask profs at a chinese university). We then pull out 10 names at random and contact the math faculty of those universities. We'll go with whatever the majority of them agree upon (actually, I'd almost be willing to bet an additional $100 that it'll be unanimous that they say .999repeating = exactly 1.

Then again, that would be followed with someone starting a thread about how 10 out of 10 randomly selected college level math programs...



Let me offer not a proof, but perhaps a visual demonstration that some of you may be able to follow (can't remember if this one was shown yet or not)

2/7 = .285714285714285714285714285714285714285714285714285714...
5.7 = .714285714285714285714285714285714285714285714285714285...

Note: 2/7 + 5/7 equals exactly 1
Now, notice what happens if you were to add the two.
you get .99999999999999999999999999999999 repeating forever.

your demonstration is flawed, consider this
does 2/7 really equal .285714285714285714285714285714285714285714285714285714... and 5/7 equal .714285714285714285714285714285714285714285714285714285...?
it's the same question, does 1/1 really equal 0.99999.................?
2/7 and 5/7 are 100% accurate values, there is no approximation, they are EXACT values, so therefore when added produce 1.
But you converted them into decimals, and repeating decimals are inherently inaccurate, because they are infinite. And we can't work with infinity, so eventually they get cut off and therefore produce errors, so when u add 2 repeating decimals together, naturally the result would have an error percentage, which causes it to not equate 1.
Remember back in high school when teachers asked u to always keep answers in fraction form until the last step then round?

AHHHHH, so you ADMIT that .9999... = 1. Wake up! Look at what I put in bold. Apparently you don't realize that we're talking about the INFINITELY long string of 9's. We never said anything about stopping it somewhere so that you can work with it in your calculator or computer. The error (the difference between .999... and 1) = 0 before you terminate the infinitely repeating decimal. The infinitely repeating decimal does indeed = 1. And, once you terminate it someplace, THEN it differs by 1x10^-n where n is the number of 9's in the truncated decimal. BUT, no one here thinks that the terminated decimal =1.

edit: ooops, missed a /b

I'm still not entirely convinced, 0.99999 repeating infintely is still 0.999999...it'll never actually turn into 1. the concept of infinity is difficult to grasp, perhaps some brilliant mind will invent a second calculus to further our understanding of the universe.

 

[josphII]

...repeating decimals are inherently inaccurate, because they are infinite. And we can't work with infinity, so eventually they get cut off and therefore produce errors...

wrong

I'm still not entirely convinced, 0.99999 repeating infintely is still 0.999999...it'll never actually turn into 1. the concept of infinity is difficult to grasp, perhaps some brilliant mind will invent a second calculus to further our understanding of the universe.

turn into 1? not sure what you mean by that. if you look at the proof .999... most definetely "turns into 1"

 

[matt426malm]

Originally posted by: josphII

...repeating decimals are inherently inaccurate, because they are infinite. And we can't work with infinity, so eventually they get cut off and therefore produce errors...

wrong

I'm still not entirely convinced, 0.99999 repeating infintely is still 0.999999...it'll never actually turn into 1. the concept of infinity is difficult to grasp, perhaps some brilliant mind will invent a second calculus to further our understanding of the universe.

turn into 1? not sure what you mean by that. if you look at the proof .999... most definetely "turns into 1"

I think that thing at the end was a way of saying yah I was wrong with out actually saying it.

 

[silverpig]

Originally posted by: MaxFusion16

Originally posted by: silverpig

Originally posted by: MaxFusion16

Originally posted by: silverpig
2 = 2.00000...

Is it not exact?

ok this is getting silly, if there is nothing other than 0s after the decimal point, then y even put the 0s there, it's just stupid. But if we are talking about significant figures, then no it's not exact, cuz significant figures is rounding, you are rounding the number to within an acceptable error percentage.

The zeros are always there, we just don't write them. I was trying to illustrate that you're going about this without thinking about it. Look at this:

2.000... - 2.000... = 0.000...
1.000... - 0.999... = 0.000...

did u not just disprove yourself?
if 1.00000 - 0.99999 = something, then 1 can't be equal to 0.99999 since there is something in between them.

No, I absolutely did not. Look at it again. It says the difference is 0. At least, the difference is the same as the difference between 2 and 2. If you accept 2 being the same number as 2, and they have no difference, then you have to accept 1 being the same as 0.999... as there is no difference there either. I have no idea how you managed to take my post as saying there is a difference.

 

[silverpig]

No number "turns into" anything else. Numbers are values, not functions. They don't vary. 0.999... does not become 1, it IS 1. 4/2 does not become 2, it IS 2. 2 does not become 3, it's just NOT 3.

 

[GoodToGo]

The idea of addding fractions to equal one is inherently flawed. Someone mentioned that

1/3 + 1/3 + 1/3 = 1

or that

0.33333333333... + 0.33333333333... + 0.33333333333... = 1

So basically they are saying that 1/3 = 0.33333333333...

But something very interesting happens when you multiply both sides by 3.

You come up with 1 = 0.99999999999...

So in order to prove that 1 = 0.99999999999... you start with the same assumption? That of course is very very wrong. The same can be said with any fractions whether it is 1/3 or 2/7 or whatever.

Also the idea of subtracting irrational numbers from one another is wrong. Say I have an irrational number and consider that only 10 digits are significant. If I multiply it by 10 then I have only 9 digits after the decimal place. So when I subtract one from the another I have a discrepancy at the 10th digit after the decimal place and it will NOT be zero. Of course then the argueent comes up that irrational numbers go on till infinity. Fair enough. If you can correlate the same analogy as above with infinite decimal places and infinite + 1 decimal places, the proof will make sense.

 

[silverpig]

The infinite + 1th place huh?

 

[silverpig]

Originally posted by: GoodToGo
The idea of addding fractions to equal one is inherently flawed. Someone mentioned that

1/3 + 1/3 + 1/3 = 1

or that

0.33333333333... + 0.33333333333... + 0.33333333333... = 1

So basically they are saying that 1/3 = 0.33333333333...

But something very interesting happens when you multiply both sides by 3.

You come up with 1 = 0.99999999999...

So in order to prove that 1 = 0.99999999999... you start with the same assumption? That of course is very very wrong. The same can be said with any fractions whether it is 1/3 or 2/7 or whatever.

Also the idea of subtracting irrational numbers from one another is wrong. Say I have an irrational number and consider that only 10 digits are significant. If I multiply it by 10 then I have only 9 digits after the decimal place. So when I subtract one from the another I have a discrepancy at the 10th digit after the decimal place and it will NOT be zero. Of course then the argueent comes up that irrational numbers go on till infinity. Fair enough. If you can correlate the same analogy as above with infinite decimal places and infinite + 1 decimal places, the proof will make sense.

1/3 does equal 0.333... Do the long division if you don't believe me.

You can long divide 1 into 1 and show that 1 = 0.999... as well.

 

[GoodToGo]

Originally posted by: silverpig

Originally posted by: GoodToGo
The idea of addding fractions to equal one is inherently flawed. Someone mentioned that

1/3 + 1/3 + 1/3 = 1

or that

0.33333333333... + 0.33333333333... + 0.33333333333... = 1

So basically they are saying that 1/3 = 0.33333333333...

But something very interesting happens when you multiply both sides by 3.

You come up with 1 = 0.99999999999...

So in order to prove that 1 = 0.99999999999... you start with the same assumption? That of course is very very wrong. The same can be said with any fractions whether it is 1/3 or 2/7 or whatever.

Also the idea of subtracting irrational numbers from one another is wrong. Say I have an irrational number and consider that only 10 digits are significant. If I multiply it by 10 then I have only 9 digits after the decimal place. So when I subtract one from the another I have a discrepancy at the 10th digit after the decimal place and it will NOT be zero. Of course then the argueent comes up that irrational numbers go on till infinity. Fair enough. If you can correlate the same analogy as above with infinite decimal places and infinite + 1 decimal places, the proof will make sense.

1/3 does equal 0.333... Do the long division if you don't believe me.

You can long divide 1 into 1 and show that 1 = 0.999... as well.

Nope, 1/3 does not equal 0.333...... It is only approximated by 0.333..... No one wants to sit and write pages and pages of 3's while writing out the full form of 1/3 so they just approximate it by 0.333..... I am not sure I follow you in your long division of 1 by 1. Also you still did not refute the fact that when I multiply both sides by 3, we get the same thing that we are trying to prove.

Also if I replace infinity by 10^24, would it satisfy you? I am just trying to make a simple point there but used a concept instead of a real number.

 

[matt426malm]

Originally posted by: GoodToGo

Originally posted by: silverpig

Originally posted by: GoodToGo
The idea of addding fractions to equal one is inherently flawed. Someone mentioned that

1/3 + 1/3 + 1/3 = 1

or that

0.33333333333... + 0.33333333333... + 0.33333333333... = 1

So basically they are saying that 1/3 = 0.33333333333...

But something very interesting happens when you multiply both sides by 3.

You come up with 1 = 0.99999999999...

So in order to prove that 1 = 0.99999999999... you start with the same assumption? That of course is very very wrong. The same can be said with any fractions whether it is 1/3 or 2/7 or whatever.

Also the idea of subtracting irrational numbers from one another is wrong. Say I have an irrational number and consider that only 10 digits are significant. If I multiply it by 10 then I have only 9 digits after the decimal place. So when I subtract one from the another I have a discrepancy at the 10th digit after the decimal place and it will NOT be zero. Of course then the argueent comes up that irrational numbers go on till infinity. Fair enough. If you can correlate the same analogy as above with infinite decimal places and infinite + 1 decimal places, the proof will make sense.

1/3 does equal 0.333... Do the long division if you don't believe me.

You can long divide 1 into 1 and show that 1 = 0.999... as well.

Nope, 1/3 does not equal 0.333...... It is only approximated by 0.333..... No one wants to sit and write pages and pages of 3's while writing out the full form of 1/3 so they just approximate it by 0.333..... I am not sure I follow you in your long division of 1 by 1. Also you still did not refute the fact that when I multiply both sides by 3, we get the same thing that we are trying to prove.

Also if I replace infinity by 10^24, would it satisfy you? I am just trying to make a simple point there but used a concept instead of a real number.

since when does 1/3 not equal 0.33333.... it is not an approximation it does equal 0.33333.... The proof is 1/3+1/3+1/3=1 AND 1/3=.333333....... so therefore 1/3 + 1/3 +1/3 = .333333.... + .333333..... + .33333...... next .33333..... + .33333.... +.333333..... = .999999...... so finally we come back to what does 1/3 + 1/3 +1/3 = .99999... or 1

there is nothing more that's how it goes .9999....=1 end of story period

 

[RossGr]

Originally posted by: GoodToGo

Originally posted by: silverpig

Originally posted by: GoodToGo
The idea of addding fractions to equal one is inherently flawed. Someone mentioned that

1/3 + 1/3 + 1/3 = 1

or that

0.33333333333... + 0.33333333333... + 0.33333333333... = 1

So basically they are saying that 1/3 = 0.33333333333...

But something very interesting happens when you multiply both sides by 3.

You come up with 1 = 0.99999999999...

So in order to prove that 1 = 0.99999999999... you start with the same assumption? That of course is very very wrong. The same can be said with any fractions whether it is 1/3 or 2/7 or whatever.

Also the idea of subtracting irrational numbers from one another is wrong. Say I have an irrational number and consider that only 10 digits are significant. If I multiply it by 10 then I have only 9 digits after the decimal place. So when I subtract one from the another I have a discrepancy at the 10th digit after the decimal place and it will NOT be zero. Of course then the argueent comes up that irrational numbers go on till infinity. Fair enough. If you can correlate the same analogy as above with infinite decimal places and infinite + 1 decimal places, the proof will make sense.

1/3 does equal 0.333... Do the long division if you don't believe me.

You can long divide 1 into 1 and show that 1 = 0.999... as well.

Nope, 1/3 does not equal 0.333...... It is only approximated by 0.333..... No one wants to sit and write pages and pages of 3's while writing out the full form of 1/3 so they just approximate it by 0.333..... I am not sure I follow you in your long division of 1 by 1. Also you still did not refute the fact that when I multiply both sides by 3, we get the same thing that we are trying to prove.

Also if I replace infinity by 10^24, would it satisfy you? I am just trying to make a simple point there but used a concept instead of a real number.

Perhaps you do not recognize the meaning of the ellipsis. The three dot represent the presence of an infinitly repeating sequence. .333... is EXACTLY 1/3 THat is the whole point of a REPRESENATION of an infinite string.

3* Sum .1^n for n = 1 to N where N is some integer is an approximation to 1/3, the bigger N the better the approximation. In the limit of N= Infinty we have equality. This is a basic definition of a limit. The ellipsis at the end of a number indicates that the limit has been taken, it represents the niumber consisting on an infinte stirng of 3s or 9s or whatever. It does not represent a sequence of numbers approaching an infinite number of digits in represents the infinite number of digit.

It really does not matter that we will never be able to write all of the digits, that is not a requirement of our number system. The beatuy and strength of mathematics is that it enables us to deal with many concepts which cannot be physically realized. We are able of examining the properties of things like Tachyons, by playing with mathemtics of systems which are not physically realizable. All of string theory is a mathematical construct which may or may not correspond to physical reality. To deny math the ability to represent and manipulate quanities and ideas which are not phyiscally realizable is simply to deny much of modern science.

 

[RossGr]

Hey cool! I got a double post!

 

[MadRat]

Anyone that believes 1/3 = .333... can apparently just corrupt the definitions of any value to mean anything.

We cannot use .333... to define a real number because the decimal is limitless. Definitions must fit within finite limits. Infinite is not bound by a limit, therefore .333... <> 1/3.

Mathematicians that defy the finite boundaries of Philosophy are not true scientists, but rather more like New Age witchdoctors. Corrupting definitions to fit an argument is not accepted logic. I believe the tact is referred to as fallacy. You .999...=1 believers are guilty of the simple crime of presumption. Hasty generalizations have been concocted to make false statements appear legitimate. Sweeping generalizations have been proposed for definitions that ignore peculiarities of each case. And the facts of the case have been repeatedly evaded using circular argument for sake of argument. Disorting facts to win an argument is a slippery slope from which to build your future.

 

[silverpig]

Originally posted by: GoodToGo

Originally posted by: silverpig

Originally posted by: GoodToGo
The idea of addding fractions to equal one is inherently flawed. Someone mentioned that

1/3 + 1/3 + 1/3 = 1

or that

0.33333333333... + 0.33333333333... + 0.33333333333... = 1

So basically they are saying that 1/3 = 0.33333333333...

But something very interesting happens when you multiply both sides by 3.

You come up with 1 = 0.99999999999...

So in order to prove that 1 = 0.99999999999... you start with the same assumption? That of course is very very wrong. The same can be said with any fractions whether it is 1/3 or 2/7 or whatever.

Also the idea of subtracting irrational numbers from one another is wrong. Say I have an irrational number and consider that only 10 digits are significant. If I multiply it by 10 then I have only 9 digits after the decimal place. So when I subtract one from the another I have a discrepancy at the 10th digit after the decimal place and it will NOT be zero. Of course then the argueent comes up that irrational numbers go on till infinity. Fair enough. If you can correlate the same analogy as above with infinite decimal places and infinite + 1 decimal places, the proof will make sense.

1/3 does equal 0.333... Do the long division if you don't believe me.

You can long divide 1 into 1 and show that 1 = 0.999... as well.

Nope, 1/3 does not equal 0.333...... It is only approximated by 0.333..... No one wants to sit and write pages and pages of 3's while writing out the full form of 1/3 so they just approximate it by 0.333..... I am not sure I follow you in your long division of 1 by 1. Also you still did not refute the fact that when I multiply both sides by 3, we get the same thing that we are trying to prove.

Also if I replace infinity by 10^24, would it satisfy you? I am just trying to make a simple point there but used a concept instead of a real number.

As has been pointed out already, the ... represents an infinite string of digits.

 

[RossGr]

Originally posted by: MadRat
Anyone that believes 1/3 = .333... can apparently just corrupt the definitions of any value to mean anything.

We cannot use .333... to define a real number because the decimal is limitless. Definitions must fit within finite limits. Infinite is not bound by a limit, therefore .333... <> 1/3.

Mathematicians that defy the finite boundaries of Philosophy are not true scientists, but rather more like New Age witchdoctors. Corrupting definitions to fit an argument is not accepted logic. I believe the tact is referred to as fallacy. You .999...=1 believers are guilty of the simple crime of presumption. Hasty generalizations have been concocted to make false statements appear legitimate. Sweeping generalizations have been proposed for definitions that ignore peculiarities of each case. And the facts of the case have been repeatedly evaded using circular argument for sake of argument. Disorting facts to win an argument is a slippery slope from which to build your future.

Seems to me that you are the witch docter, dening the existance of modern medicin.

I do not BELIEVE that 1 =.999..., I have knowledge of the structure of the Real Number system and I KNOW that 1 =.999... You, on the other hand, BELIEVE that it is not. Since you are unable to seperate believe and knowledge, we have this unending disscussion.

 

[MadRat]

Good, then spare us 32 more pages of "discussion" and define your explanation without corrupting the meanings behind your tools.

 

[silverpig]

Originally posted by: MadRat
Good, then spare us 32 more pages of "discussion" and define your explanation without corrupting the meanings behind your tools.

Basically:

If you add ANYTHING, no matter how small to 0.999... the sum will be larger than 1. If you subtract ANYTHING, no matter how small from 0.999... the answer will always be less than 1.

 

[FelixDeCat]

Can we lock this thread already?

 

[silverpig]

Why lock it?

"Oh can someone please lock this thread? I just can't help but click on it and post about how I want it to die. There is no possibility of me just ignoring it, so I need someone to lock it for me. Forget about all the posters who actually contribute to the discussion, I just don't like it."

 

[RossGr]

Originally posted by: MadRat
Good, then spare us 32 more pages of "discussion" and define your explanation without corrupting the meanings behind your tools.

Many words but no content. Once again because you are unable to address the mathematics at anything other then a 6th grade level you aviod the real issues.

 

[Chu]

omg . . . this thread is still alive?

I don't feal like reading through 32 pages of argument, but considering from when I was reading this thread a while ago and the last page, I assume it's pretty much all the same.

The people who don't believe this is false are probably all falling into the same trap. Infinity is a quantum leap past any other number. By manipulating discreet values, you cannot get there. If you remember doing inductive proofs back in high school, it's the same reason that you can show something holds for all k, but not for infinity. .9999999... is just incredibly bad notation. It makes it look like you do eventuially get to infinity -- and for this reason is incredibly misleading. You just can't use your intuition for dealing with infinity, because our brains are not wired for it. Even after more then a semesters worth of Real Analysis, some math majors still don't get that you can never get to infinity.

-Chu

 

[FelixDeCat]

Originally posted by: silverpig
Why lock it?

"Oh can someone please lock this thread? I just can't help but click on it and post about how I want it to die. There is no possibility of me just ignoring it, so I need someone to lock it for me. Forget about all the posters who actually contribute to the discussion, I just don't like it."

Its stupid. Like you. Or like the chicken vs. the egg argument. It will never end, but this thread should.:|

 

[ViviTheMage]

wow, big post...ill have to say no though.

 

[Kyteland]

To those saying that 1/3 != 0.3333.... try doing the long division. They are the same.
...0.33333333333333...
3|1.00000000000000...
......9
......10
........9
........10
..........9
..........10
............9
............10
..............9
..............10
................9
................10
..................9
..................10
....................9
....................10
......................9
......................10
........................9
........................10
..........................9
..........................1

etc.

 

[silverpig]

Originally posted by: FelixDeKat

Originally posted by: silverpig
Why lock it?

"Oh can someone please lock this thread? I just can't help but click on it and post about how I want it to die. There is no possibility of me just ignoring it, so I need someone to lock it for me. Forget about all the posters who actually contribute to the discussion, I just don't like it."

Its stupid. Like you. Or like the chicken vs. the egg argument. It will never end, but this thread should.:|

Your parents must be proud.