Poll: 0.999... = 1

[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.

 

[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&#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

Oh thank god.

Having read through a good majority of this thread, it becomes REALLY hard to tell which posts are jokes. Still, I give it a 10 for brilliant trolling.

 

[Rabid Toilet]

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.

And yet we have imaginary numbers, we have pi. These aren't real, they aren't there, and yet we accept that they exist, that we can use them, and that they are true.

 

[popa_qwerty]

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 counterintelligence 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.

and this world of empty space is nothing but what we conseve it to be

ps pardon my bad English

 

[JoshGod]

That is not hard maths. I learnt that at the latest at GCSE.

 

[orangeapples]

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?

ummm... that's not what I meant. the difference between you and you losing a strand of hair is so small that it pretty much does not exist. you are (1 whole) - (1 strand of hair). The strand of hair is small enough to not make a difference. You are still 1 whole.

in the example you make, the germ is the 1 whole, therefore it (no matter how small) exists.

 

[Lyx]

Simple reason to ignore the "proofs" for 0.9999 to equal 1 is this:

The definition of "infinity".

When i to any halfway sane person say "0. and then add an infinite amount of 9's" then by golly, all that will follow WILL be 9's. Infinite times 9 means infinite times 9. Any PHD that claims otherwise can go fuck themselves and die in a corner, for abusing authority to claim that a tautology is false.

How they are "proving" that 0.999... is equal to 1, is be REDEFINING infinity and the rules to handle it. In other words, they keep the words, but change the meaning. That is called cheating.

With this, i do not mean to say that there is no reason for changing the meanings. There may well be - but if you change the meaning, then please also change the words, because else you're quite simply deceiving people.

If for example we hypothetically were to define "@n" to mean "as close as possible to n", then 0.9 associated with the operator @1 would indeed mean "well, here we have 0.9, make that as close as possible to 1", and obviously, the ideal return value would indeed be 1. Which is quite different to saying "infinite times 9". There are other ways to achieve it. I dont care which one they use, its all fine by me, as long as what the symbols mean equals how they are used.

Or we could go the metaphysics route, by questioning if a value can even be infinitely precise, and if there always for practical reasons will be some inaccuracy. That too is okay by me.

But FFS, do not say "infinite times 9", and then do something else.

 

[Rabid Toilet]

Simple reason to ignore the "proofs" for 0.9999 to equal 1 is this:

The definition of "infinity".

When i to any halfway sane person say "0. and then add an infinite amount of 9's" then by golly, all that will follow WILL be 9's. Infinite times 9 means infinite times 9. Any PHD that claims otherwise can go fuck themselves and die in a corner, for abusing authority to claim that a tautology is false.

How they are "proving" that 0.999... is equal to 1, is be REDEFINING infinity and the rules to handle it. In other words, they keep the words, but change the meaning. That is called cheating.

With this, i do not mean to say that there is no reason for changing the meanings. There may well be - but if you change the meaning, then please also change the words, because else you're quite simply deceiving people.

If for example we hypothetically were to define "@n" to mean "as close as possible to n", then 0.9 associated with the operator @1 would indeed mean "well, here we have 0.9, make that as close as possible to 1", and obviously, the ideal return value would indeed be 1. Which is quite different to saying "infinite times 9". There are other ways to achieve it. I dont care which one they use, its all fine by me, as long as what the symbols mean equals how they are used.

Or we could go the metaphysics route, by questioning if a value can even be infinitely precise, and if there always for practical reasons will be some inaccuracy. That too is okay by me.

But FFS, do not say "infinite times 9", and then do something else.

I suppose it's true that the terminology could be confusing people, because if there's nothing but nines, how can it be one?

That doesn't change the fact that an infinite amount of nines means the distance between it and one is infinitely small, which makes them the same number.

Regardless, I've been at this for four hours, and by golly, I'm going to bed!

 

[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.

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.

And yet we have imaginary numbers, we have pi. These aren't real, they aren't there, and yet we accept that they exist, that we can use them, and that they are true.

FYI pi is a real number pi is the ratio of the circumference to the radius of the same circle
imaginary numbers are negative square root and do not cross the x intercept i think

 

[quhouv vhqwiufv qwiu]

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 prefer:

b0.b1b2b3b4... = b0 + b1(1/10) + b2(1/10)^2 + b3(1/10)^3 + b4(1/10)^4 ...

if |r| < 1 then kr + kr^2 + kr^3 + ... = kr/(1-r)

So for 0.9...:

0.(9) = 9(1/10) + 9(1/10)^2 + 9(1/10)^3 + ... = (9(1/10))/(1-(1/10)) = 1

Is that inductive proof? I'm having trouble with the formatting.

Regardless this is a well accepted fact and I disagree with the notion that it is counter-intuitive. It simply demonstrates the issues infinity proposes. There have been many threads on this topic, all of which continued on for many many pages where people repeated the same questions and answers. Have fun

Sorry I didn't format it very well :|. I think another member translated it into words earlier.