Poll: 0.999... = 1

[Coldie]

I'm not saying that there arent other good ideas backing it up to be "true." I'm just saying that this is the same logic that explains how the holocaust started. Someone of authority said something was right, and the people followed.

and dont tell me it has nothing to do with this, because it has everything to do with the reasoning behind as to why some believe its right and others dont.

Fantastic. A math thread Godwin'd in 275 posts.

Congratulations or something.

 

[zoulza]

if .9999...=1

now by that logic i can say all numbers are close to infinite

0=.11111...=.22222...=.333333...=.4444444...=.5555555...=.6666666....=.77777777...=.88888888...=.999999999...=.1=1.1111111...
so 0=infinite
and this is not true but by your logic it is

and FYI the number between .99999 and 1 is a number we call i or a imaginary number

1/3≈.33333 not 1/3=3 that is because there is no way to get .333...back to 1/3 you can try you will always fail

i open account just to answer this yay my first post

I laughed for about a five minutes after reading that. A+

 

[Rabid Toilet]

I'm not saying that there arent other good ideas backing it up to be "true." I'm just saying that this is the same logic that explains how the holocaust started. Someone of authority said something was right, and the people followed.

and dont tell me it has nothing to do with this, because it has everything to do with the reasoning behind as to why some believe its right and others dont.

Fantastic. A math thread Godwin'd in 275 posts.

Congratulations or something.

I thought about pointing that out, but decided it was too easy.

 

[smithy_2045]

Infinity doesn't scare us at all, which is why we do math with it on a regular basis.

And it actually equals both .999... and 1, but that's semantics.

1/3 = .333...
.333... * 3 = .999...
1/3 * 3 = 3/3
3/3 = 1

.999... = 1

Actually, someone made a very good point that human mathematics are very primitive and .3333... is just the best way to explain 1/3 in "rational" numbers. But it's not truly 1/3. Just the closest you can get.

In other words, .3333 != 1/3

That's because .3333 = 3333/10000 =/= 1/3

 

[orangeapples]

yes, but not at the same time. Because 02 = 0. But 12 =/= 0. Which is what the persons said when he said that .999... = 1 at the same time, both being X. You cant plug two separate values at the same, so while x = 1 and 0, it can not equal them at the same time.

While a variable can have any number of values, you cannot substitute different values of the same variable into the same set of equations, yes. X does equal to 0 and 1 at the same time, but if you resolve the variable into a number, please resolve it the same way for all instances.

However, nobody actually substituted x = 1 into any equations in the original proof. The only substitution was x = 0.(9), which is the definition of x. The equations created after said substitution eventually prove that 1 = 0.(9) = x.

Well, I was using example in this post. Which is far from the original.

ANd thats exactly what I'm saying. it cant, which is what I said.

that's not the point. in the problem you are looking at:x^2=x can equal 1 and 0
1^2=1
0^2=0

in this situation, 0 and 1 are not interchangeable which I think is what you are trying to say. What the person who brought up this problem was trying to say is that 2 things can represent the same thing: 1 can be x and 0 can be x

with the topic's problem, the question is: is .999 = 1? yes or no?

people are using 2 different approaches.
1: using methods to show that using the same logic with the same numbers you can end up with 1 and .999...
-3(1/3) = 3(.333...)
2: showing that the difference between .999... and 1 is so small that it practically does not exist.
-the guy with the limits and such. I didn't read it.

with these 2 approaches 1 and .999... are so similar that they can just be the same thing.

numbers are a human creation to conceptualize quantities. numbers are not Absolutes. Numbers are tools.

to serve its function, .999... and 1 both represent the same idea.

assume you are you. if you lose 1 strand of hair, are you still you?

technically not the exact same you, but the difference is so small that it does not really matter.

 

[IMakeIce]

You know, come to think of it, I'm surprised that web forums don't have some kind of automatic function to destroy threads like this at inception.

Blizzard literally had to start banning people to stop this conversation clogging the battle.net forums when they posted the proof as an april fools joke years and years ago. I don't know if the april fools joke was that the proof was real...or that they knew people would go ape!@#! over it...

Really? Intelligent people shouldn't be punished for the ignorance of unintelligent people. If that were to happen to me I would take the administrators to court.

For a so-called intelligent person, taking the administrators to court would be an incredibly dumb move.

I probably wouldn't win, and I accept that but I would still do it on principal, that principal being that fact is imperatively true regardless of how many people believe it and fact must not be silenced due to opposition.

They silenced it because it was disrupting the ability for other discussions to commence. At the time they outlawed it, there had been something like _hundreds_ of threads created and thousands of posts in the main thread discussing it.

More of a "Damn...we have created a monster." rather than a "Stop having discussion!"

That and the "discussion" (like we see so often on the intertubez) devolved into each side slamming eachother because the other was just _wrong_ and an idiot for it.

Oh, well that's completely different. I thought you were referring to a situation like this one.

Nah.

And actually, my information was slightly flawed. They banned it after years of it being discussed (it would die for a few months and reappear, in exactly the same fashion...several - multitudes of threads much like this one), which always devolved into hurling insults. They finally opened the can of worms with the april fools joke because so many people were made aware of it and flocked in droves to discuss it in the general forum. After that, it was not to be repeated because of the backlash it caused.

 

[emeraldrafael]

Snip

Considering how you tore into the one poster, I wouldnt go calling any kettles black.

Also, no, I'm just stating. The reasons ideas become fact is cause the idea carries in the human mind. If i were to kill everyone who thinks .999...! = 1 (not a threat) and the idea died with them, then the truth would be .999...! doesnt equal 1 because no one would beleive it. Again, I'm going to have to wait till my math professor gets back to me, I just thought it was interesting that thats why students who carry the ideas after the teacher is dead accept the idea.

 

[zoulza]

I'm not saying that there arent other good ideas backing it up to be "true." I'm just saying that this is the same logic that explains how the holocaust started. Someone of authority said something was right, and the people followed.

and dont tell me it has nothing to do with this, because it has everything to do with the reasoning behind as to why some believe its right and others dont.

I think it has more to do with the fact that people who believe they're right have actually taken higher level math courses and know what they're talking about, whereas those who disagree think infinitesimals exist when they don't.

Also, did you just bring up the holocaust in the middle of a math discussion? -facepalm-

 

[Jaime_Wolf]

Snip

I'm not saying that there arent other good ideas backing it up to be "true." I'm just saying that this is the same logic that explains how the holocaust started. Someone of authority said something was right, and the people followed.

and dont tell me it has nothing to do with this, because it has everything to do with the reasoning behind as to why some believe its right and others dont.

Also:

if .9999...=1

now by that logic i can say all numbers are close to infinite

0=.11111...=.22222...=.333333...=.4444444...=.5555555...=.6666666....=.77777777...=.88888888...=.999999999...=.1=1.1111111...
so 0=infinite
and this is not true but by your logic it is

and FYI the number between .99999 and 1 is a number we call i or a imaginary number

1/3≈.33333 not 1/3=3 that is because there is no way to get .333...back to 1/3 you can try you will always fail

You lack the pseudo-science and amateur philosophy of some of the other posters, but the mathematics is cute. I would give it an 8, but the hilarious appeal to i really makes the post.

10.

I'm glad that we can make fun of others in the thread.

How can you possibly say that this is all appeal to authority when people have posted numerous proofs? Unless you've found an error in the proofs that's, well, proof.

Addressing your other concern, this thread is using a well-known, well-studied defect in naive mathematical reasoning to provoke ignorant responses. It is, by any reasonable measure, designed wholly for the sake of making fun of others. I suppose that most of the people are just doing it silently. In that respect, I really am sorry for actually coming out and saying it, which I suppose is a little bit worse since doing it silently doesn't necessarily make anyone feel bad. I mean this sincerely.

As for yourself, the post I quoted earlier had an authoritative and downright preachy tone. Generally, you want to avoid such tones unless you really, really know you're right. And now you're comparing it to the HOLOCAUST? That's just bad taste and makes me feel a little less sorry about before.

Edit: On the one hand, I'm happy that you're talking to a professor. On the other hand, are you seriously posting about talking to a professor RIGHT AFTER explaining how appeals to authority are dangerous?

 

[Rabid Toilet]

*snip*

I appreciate the effort, but that's not "quite" what we are arguing.

We aren't saying that the distance is so small that it may as well be zero, so they are pretty much the same number.

We're saying that the distance is zero, and that they are exactly the same number, without rounding or approximations.

 

[emeraldrafael]

yes, but not at the same time. Because 02 = 0. But 12 =/= 0. Which is what the persons said when he said that .999... = 1 at the same time, both being X. You cant plug two separate values at the same, so while x = 1 and 0, it can not equal them at the same time.

While a variable can have any number of values, you cannot substitute different values of the same variable into the same set of equations, yes. X does equal to 0 and 1 at the same time, but if you resolve the variable into a number, please resolve it the same way for all instances.

However, nobody actually substituted x = 1 into any equations in the original proof. The only substitution was x = 0.(9), which is the definition of x. The equations created after said substitution eventually prove that 1 = 0.(9) = x.

Well, I was using example in this post. Which is far from the original.

ANd thats exactly what I'm saying. it cant, which is what I said.

that's not the point. in the problem you are looking at:x^2=x can equal 1 and 0
1^2=1
0^2=0

in this situation, 0 and 1 are not interchangeable which I think is what you are trying to say. What the person who brought up this problem was trying to say is that 2 things can represent the same thing: 1 can be x and 0 can be x

with the topic's problem, the question is: is .999 = 1? yes or no?

people are using 2 different approaches.
1: using methods to show that using the same logic with the same numbers you can end up with 1 and .999...
-3(1/3) = 3(.333...)
2: showing that the difference between .999... and 1 is so small that it practically does not exist.
-the guy with the limits and such. I didn't read it.

with these 2 approaches 1 and .999... are so similar that they can just be the same thing.

numbers are a human creation to conceptualize quantities. numbers are not Absolutes. Numbers are tools.

to serve its function, .999... and 1 both represent the same idea.

assume you are you. if you lose 1 strand of hair, are you still you?

technically not the exact same you, but the difference is so small that it does not really matter.

YES! Cause something's missing! What if I lost a toenail? You justs aid that they are different, its just thats tiny. Germs are tiny, do they not exist?

 

[Redingold]

M'kay. The number 0.999... is equal to an infinite series 0.9 + 0.09 + 0.009 + 0.0009 and so on. If you know anything about slightly advanced maths, you'll know that the sum of an infinite geometric series is equal to a/(1-r) when |r| < 1 (explained below for those who aren't so good at maths)

In our example here, a, the first term, is 0.9, and r, the common ratio, is 0.1 (because each term is the previous term multiplied by 0.1).

So we have 0.9/(1-0.1) which equals 0.9/0.9 which equals 1.

Explanation of maths involved:

A geometric sequence is one where each term is the previous term multiplied by some number r. The first term is a, the second term is ar, the third term is ar[sup]2[/sup] and so on. The nth term is ar[sup]n-1[/sup].

The sum of a geometric series to n terms, which we shall call S[sub]n[/sub], is therefore equal to a + ar + ar[sup]2[/sup]...+ ar[sup]n-2[/sup] + ar[sup]n-1[/sup]

Multiplying by r, we get rS[sub]n[/sub] = ar + ar[sup]2[/sup] + ar[sup]3[/sup]...+ ar[sup]n-1[/sup] + ar[sup]n[/sup]

Subracting rS[sub]n[/sub] from S[sub]n[/sub] leads to S[sub]n[/sub] - rS[sub]n[/sub] = a - ar[sup]n[/sup]

This means S[sub]n[/sub](1-r) = a(1 - r[sup]n[/sup])

And S[sub]n[/sub] = a(1 - r[sup]n[/sup])/(1-r)

Now, to find the sum to infinity, n must be equal to infinity. If |r| > 1, r[sup]infinity[/sup] is infinite. If |r| < 1, r[sup]infinity[/sup] is equal to zero. (If |r| = 1, we end up with 0/0, and I don't wanna go there (it's not 1)).

Thus, S[sub]infinity[/sub] = a(1 - r[sup]infinity[/sup])/(1-r) = a(1-0)/(1-r) = a/(1-r) when |r| < 1

Satisfied now?

Unfortunately, we've used that proof at least twice, to no avail. Good effort though!

Seriously? Twice? To no avail?

Wow, that's just awful.

You've let me down, Escapist.

 

[emeraldrafael]

I'm not saying that there arent other good ideas backing it up to be "true." I'm just saying that this is the same logic that explains how the holocaust started. Someone of authority said something was right, and the people followed.

and dont tell me it has nothing to do with this, because it has everything to do with the reasoning behind as to why some believe its right and others dont.

I think it has more to do with the fact that people who believe they're right have actually taken higher level math courses and know what they're talking about, whereas those who disagree think infinitesimals exist when they don't.

Also, did you just bring up the holocaust in the middle of a math discussion? -facepalm-

Cause there's Controversy.

Oh, yeah, I had reason. Its just hard to find controversy on a naturally huge thing. So all of those who criticized me, lets here what your examples would be. Dicks.

 

[popa_qwerty]

Snip

I'm not saying that there arent other good ideas backing it up to be "true." I'm just saying that this is the same logic that explains how the holocaust started. Someone of authority said something was right, and the people followed.

and dont tell me it has nothing to do with this, because it has everything to do with the reasoning behind as to why some believe its right and others dont.

Also:

if .9999...=1

now by that logic i can say all numbers are close to infinite

0=.11111...=.22222...=.333333...=.4444444...=.5555555...=.6666666....=.77777777...=.88888888...=.999999999...=.1=1.1111111...
so 0=infinite
and this is not true but by your logic it is

and FYI the number between .99999 and 1 is a number we call i or a imaginary number

1/3&#8776;.33333 not 1/3=3 that is because there is no way to get .333...back to 1/3 you can try you will always fail

You lack the pseudo-science and amateur philosophy of some of the other posters, but the mathematics is cute. I would give it an 8, but the hilarious appeal to i really makes the post.

10.

I'm glad that we can make fun of others in the thread.

How can you possibly say that this is all appeal to authority when people have posted numerous proofs? Unless you've found an error in the proofs that's, well, proof.

Addressing your other concern, this thread is using a well-known, well-studied defect in naive mathematical reasoning to provoke ignorant responses. It is, by any reasonable measure, designed wholly for the sake of making fun of others. I suppose that most of the people are just doing it silently. In that respect, I really am sorry for actually coming out and saying it, which I suppose is a little bit worse since doing it silently doesn't necessarily make anyone feel bad. I mean this sincerely.

As for yourself, the post I quoted earlier had an authoritative and downright preachy tone. Generally, you want to avoid such tones unless you really, really know you're right. And now you're comparing it to the HOLOCAUST? That's just bad taste and makes me feel a little less sorry about before.

come on that post was a joke lets be cool

 

[smithy_2045]

Infinity doesn't scare us at all, which is why we do math with it on a regular basis.

And it actually equals both .999... and 1, but that's semantics.

1/3 = .333...
.333... * 3 = .999...
1/3 * 3 = 3/3
3/3 = 1

.999... = 1

Actually, someone made a very good point that human mathematics are very primitive and .3333... is just the best way to explain 1/3 in "rational" numbers. But it's not truly 1/3. Just the closest you can get.

In other words, .3333 != 1/3

That's because .3333 = 3333/10000 =/= 1/3

So I forgot the put the periods down to represent repeating numbers. Clearly that shows all the flaws of my logic.

This is going nowhere. Maybe you guys should start looking for causes rather than effects.

If you're going to ignore the numerous proofs you've been given, there's no point taking you seriously.

If you feel like revising them, there's an entire wikipedia article dedicated to it. [http://en.wikipedia.org/wiki/0.999...]

 

[Rabid Toilet]

Infinity doesn't scare us at all, which is why we do math with it on a regular basis.

And it actually equals both .999... and 1, but that's semantics.

1/3 = .333...
.333... * 3 = .999...
1/3 * 3 = 3/3
3/3 = 1

.999... = 1

Actually, someone made a very good point that human mathematics are very primitive and .3333... is just the best way to explain 1/3 in "rational" numbers. But it's not truly 1/3. Just the closest you can get.

In other words, .3333 != 1/3

That's because .3333 = 3333/10000 =/= 1/3

So I forgot the put the periods down to represent repeating numbers. Clearly that shows all the flaws of my logic.

This is going nowhere. Maybe you guys should start looking for causes rather than effects.

I apologize, but there have been people on here who actually used the cut off versions of the numbers in their "proofs" that the two numbers weren't equal. Excuse us if we believed you might be one of them.

Still, 1/3 does exactly equal .333...

There is no distance between .333... and 1/3, so they are the same number. If they weren't, there would have to be a number you could add to .333... to make it closer to 1/3. The only way you could do that would be to add another 3 on to the end, but there is no end. There is already an infinite number of threes, so it is infinitely close to 1/3, which makes them the same number.

 

[Biosophilogical]

If x = 0.999999...
Then 10x = 9.9999...
Therefore, 10x - x = 9
Which implies 9x = 9
Thus, x = 1
x also = 0.99999...

In conclusion, I have just proven 1 = 0.9999...

The thing is, infinity is relative. So ...

x = 0.9999 .... to the infinite decimal place
10x = 9.9999 .... to one less infinite place value
Therefore:
10x - x = 8.9999 .... 1, where the one is in the infinite decimal place
9x = 8.9999 .... 1
8.9999 .... 1 = 0.9999 ... to the infinite decimal place

If that doesn't make sense to you, imagine two ... let's make them space ships, travelling along the same axis in the same direction at the exact same speed which will never alter. If Rocket 1 is 10 metres in front of rocket 2, and they both start at the same time, after an infinite amount of time has passed, the distance they are from rocket 2's starting point is infinity, but rocket 1 is 10 metres in front of rocket 2. Therefore, both ships have travelled an infinite distance, but the distance between the origin and rocket 1 is a greater degree of infinity (by a distance of 10 metres) than rocket 2.

You wouldn't be able to assess their positions at infinity amount of time because they would never reach it...

Maths is a representation of our reality through the use of numbers, so my rocket ship analogy-thing was basically to give a real-world example of the case of re3lative infinities. And sure, we can't measure the distance after an infinite time, but we can state that, because of the equal velocity (and therefore constant distance between the two rockets) that one is furhter away from an infinitely far point than the other.

Actually I feel I'm explaining it badly. Basically, our understanding of reality is that, under the described rocket circumstances, they will both be an infinite distance from a particular point in space[footnote]Because the concept of infinity is something which is without limits it is basically saying "If they travel for a period of time that is without a limit, they will travel a proportionally infinite distance" (proportional to velocity and initial location that is)[/footnote], but they will both be a different distance. So they are both an infinite distance, but one is more than the other. And seeing as maths is a numerical representation of our reality, then this case of 0.99999... is an example of relative infinities as expressed by the rocket example.

So basically (in case I still worded it poorly), because the nature of our perception/reality is such that infinity can be perceived as existing to degrees (as in the 'bound by physical laws' example of rocket ships) then this 'relative infinities' quality is a propery of mathematics. So, because maths is dependent upon reality, and reality supports relative infinity, then 0.999... does not equal 1.

 

[emeraldrafael]

Snip

I'm not saying that there arent other good ideas backing it up to be "true." I'm just saying that this is the same logic that explains how the holocaust started. Someone of authority said something was right, and the people followed.

and dont tell me it has nothing to do with this, because it has everything to do with the reasoning behind as to why some believe its right and others dont.

And yet someone in authority said that 2 + 2 = 4, and the people followed.

Why does 2 + 2 = 4? Because they say so.

Using the very laws of mathematics that were invented so long ago by those people, .99... and 1 are the same number.

because 2+2=4 is based on the idea of two.... somethings... apples. Two apples, plus two apples. equals four apples. Its volume, its real, its there.

 

[Glademaster_v1legacy]

If x = 0.999999...
Then 10x = 9.9999...
Therefore, 10x - x = 9
Which implies 9x = 9
Thus, x = 1
x also = 0.99999...

In conclusion, I have just proven 1 = 0.9999...

I hate this theorem worse than the making 2=1 through dividing by 0.

OT: Yes technically speaking in maths 0.9999... is equal to one. For more counterinuitive ideas. Since every atom is mostly empty space me, you, your family, the walls around you and everything you have ever known is mostly empty space. Thus everything ever is a waste of space.