Is 1 = 0.9999......

[MAME]

Originally posted by: Stefan

X = .999...

1 - X = .000...0001
1 - 1 = 0

.000...0001 != 0

therefore X != 1

therefore .999... != 1

It is irrelevent how many 9's you add to the end of the number, you are only apporaching 1 and never getting there.

Wait, 1 - X = .000...0001 ????????

What the hell? How can you have an infinite number of 0's followed by the number 1? Do you know what infinity means?

If you honestly think this is a proof, why don't you submit it to the math community and get lots of money? You would be rich.

 

[VTboy]

This is true. Here is a proof

We can think of this as

lim .9(1-10^(-m-1))/.9
m-->infinity

You can think of this as

lim (1-10^(-m-1))
m-->infinity

Now this is also the same as 1-lim 10^(-m-1)
.................................................m--->infinity

since infinity -1 =infinity then 10/(infinity-1) = 10/infinity. 10/infinity=0.

Thus 1-lim 10^(-m-1) = 1-0 = 1
..................m--->infinity

 

[BigToque]

Originally posted by: MAME

Originally posted by: Stefan

X = .999...

1 - X = .000...0001
1 - 1 = 0

.000...0001 != 0

therefore X != 1

therefore .999... != 1

It is irrelevent how many 9's you add to the end of the number, you are only apporaching 1 and never getting there.

Wait, 1 - X = .000...0001 ????????

What the hell? How can you have an infinite number of 0's followed by the number 1? Do you know what infinity means?

If you honestly think this is a proof, why don't you submit it to the math community and get lots of money? You would be rich.

The idea is that no matter where you stop, 100 9's, or 1,000,000 9's. Infinity is a placeholder for a real number. If you subtract that number from 1, you will never get 0. The result of the equation always ends with ...01.

 

[MAME]

Originally posted by: Stefan

Originally posted by: MAME

Originally posted by: Stefan

X = .999...

1 - X = .000...0001
1 - 1 = 0

.000...0001 != 0

therefore X != 1

therefore .999... != 1

It is irrelevent how many 9's you add to the end of the number, you are only apporaching 1 and never getting there.

Wait, 1 - X = .000...0001 ????????

What the hell? How can you have an infinite number of 0's followed by the number 1? Do you know what infinity means?

If you honestly think this is a proof, why don't you submit it to the math community and get lots of money? You would be rich.

The idea is that no matter where you stop, 100 9's, or 1,000,000 9's. Infinity is a placeholder for a real number. If you subtract that number from 1, you will never get 0. The result of the equation always ends with ...01.

lol, I knew you didn't know what infinity means!


INFINITY MEANS YOU DON'T STOP EVERRRRRRRRRRRRRRRRRRRR

do you understand?

if you stop, then it's not .999... now is it? YOU LOSE

 

[Rahminator]

Originally posted by: SilentRunning

Originally posted by: silverpig

I read the link, I know the difference between giving a value and finding what it equals.

The value given to 0.999... is the limit of the sum, this limit equals 1.

So you get, I thought you were one of the ones who thought 1 = 0.99999...

They are not equal but the are given the same value. That is the concept that people here do not seem to grasp. That is why my tag line is what it is. Yes 1 and 0.9999... are the same value for mathematical purposes due to the approximation for 0.9999..., but they are not truely equal.

They thread asked only one question are the two numbers equal, not do we treat them as the same value.

You're incorrect.
.99999... is a geometric series that converges at exactly 1 when you take infinitely many terms (which is what the first poster wanted to do, extend .9999 into infinity).

 

[BigToque]

Originally posted by: MAME

Originally posted by: Stefan

Originally posted by: MAME

Originally posted by: Stefan

X = .999...

1 - X = .000...0001
1 - 1 = 0

.000...0001 != 0

therefore X != 1

therefore .999... != 1

It is irrelevent how many 9's you add to the end of the number, you are only apporaching 1 and never getting there.

Wait, 1 - X = .000...0001 ????????

What the hell? How can you have an infinite number of 0's followed by the number 1? Do you know what infinity means?

If you honestly think this is a proof, why don't you submit it to the math community and get lots of money? You would be rich.

The idea is that no matter where you stop, 100 9's, or 1,000,000 9's. Infinity is a placeholder for a real number. If you subtract that number from 1, you will never get 0. The result of the equation always ends with ...01.

lol, I knew you didn't know what infinity means!


INFINITY MEANS YOU DON'T STOP EVERRRRRRRRRRRRRRRRRRRR

do you understand?

if you stop, then it's not .999... now is it? YOU LOSE

I know that it "doesn't stop" i'm saying that it doesn't matter what the number of decimal places is, at any instant for as long as you can write the number 9, you will never end up with the 2 numbers being equal.

So then by the definition of infinity, the actual answer to the question it that there is no answer to the question. In order to make the calculation, you need a finite number.

 

[MAME]

Originally posted by: Rahminator

Originally posted by: SilentRunning

Originally posted by: silverpig

I read the link, I know the difference between giving a value and finding what it equals.

The value given to 0.999... is the limit of the sum, this limit equals 1.

So you get, I thought you were one of the ones who thought 1 = 0.99999...

They are not equal but the are given the same value. That is the concept that people here do not seem to grasp. That is why my tag line is what it is. Yes 1 and 0.9999... are the same value for mathematical purposes due to the approximation for 0.9999..., but they are not truely equal.

They thread asked only one question are the two numbers equal, not do we treat them as the same value.

You're incorrect.
.99999... is a geometric series that converges at exactly 1 when you take infinitely many terms (which is what the first poster wanted to do, extend .9999 into infinity).

correct

 

[VTboy]

Another proof

.99999... = lim sum 9/10^n
.....(n -> Infinity) (n=1 )



I can prove this series converges.

I will use the Root test

lim | 9/10^n|^(1/n)
n=1 -> Infinity

= lim |9^(1/n)/10| Since we know this is less than 1 then the series converges.
n=1 -> Infinity

 

[MAME]

Originally posted by: Stefan

I know that it "doesn't stop" i'm saying that it doesn't matter what the number of decimal places is, at any instant for as long as you can write the number 9, you will never end up with the 2 numbers being equal.

So then by the definition of infinity, the actual answer to the question it that there is no answer to the question. In order to make the calculation, you need a finite number.

What? Stop talking now before you look even dumber.
You don't write the 9's, it's not some sort of .999... generating problem. The number already exists.

This should be fun, explain to me why .333... * 3 = 1 and NOT .999...

don't convert to fraction, use .333... as a decimal.

 

[BigToque]

Originally posted by: MAME

Originally posted by: Stefan

I know that it "doesn't stop" i'm saying that it doesn't matter what the number of decimal places is, at any instant for as long as you can write the number 9, you will never end up with the 2 numbers being equal.

So then by the definition of infinity, the actual answer to the question it that there is no answer to the question. In order to make the calculation, you need a finite number.

What? Stop talking now before you look even dumber.
You don't write the 9's, it's not some sort of .999... generating problem. The number already exists.

This should be fun, explain to me why .333... * 3 = 1 and NOT .999...

don't convert to fraction, use .333... as a decimal.

This is stupid.

.333... * 3 != 1
.333... * 3 == .999...

For any practical purposes the answer is yes .999... = 1.
For any other reason, this is just a good way to waste time

 

[MAME]

Originally posted by: Stefan


This is stupid.

.333... * 3 != 1
.333... * 3 == .999...

For any practical purposes the answer is yes .999... = 1.
For any other reason, this is just a good way to waste time

LOL!!!!!!!!!!!!!!!!!!!!!!!!!!!

You honestly think .333... * 3 != 1? That's the dumbest thing I've ever heard.

so that means 1/3 * 3 = 3/3 != 1


HILARIOUS

 

[VTboy]

MAME it is clear that these people are trying to destroy one of the foundations of calculus by discrediting limits.

 

[DrPizza]

Originally posted by: Stefan
Theoretically, 1 != .999...
Practically, 1 = .999...

I can't imagine some carpenter saying "Damnit Jim, you cut the fscking board to short! I said 1 meter, not .999999999999999999999999999999999 meters! Get it right!

How this reached 1900 posts is beyond me.

It reached 1900 posts because there are a bunch of mathematically impaired people who keep bumping this thread by saying that .999repeating != 1. And, the mathematically intelligent people typically hate to see innumeracy - same as illiteracy, but related to mathematics instead - flourish. Thus, the people whose brains are wired to be able to comprehend that .999... = 1 exactly keep trying to convince others of that fact, and can't figure out why other people can't comprehend it.

Fighting ignorance is a tough battle for the mathematicians. When faced with numerous mathematical proofs coming from several verified mathematical sources, you'd think that the average person would accept the fact that .999... = 1. Anything less is pure ignorance. The debate on this issue is analygous to a 5 year old arguing that there is too such a thing as the Easter Bunny. But, the ignorant masses will probably continue to attempt to provide new insight in the form of incorrect proofs based on their misunderstandings of mathematical concepts they think they've "learned," pushing this thread up to 3000 posts or more.

 

[MAME]

Originally posted by: VTboy
MAME it is clear that these people are trying to destroy one of the foundations of calculus by discrediting limits.

they're so dumb my cat is crying

 

[BigToque]

Originally posted by: MAME

Originally posted by: Stefan


This is stupid.

.333... * 3 != 1
.333... * 3 == .999...

For any practical purposes the answer is yes .999... = 1.
For any other reason, this is just a good way to waste time

LOL!!!!!!!!!!!!!!!!!!!!!!!!!!!

You honestly think .333... * 3 != 1? That's the dumbest thing I've ever heard.

so that means 1/3 * 3 = 3/3 != 1


HILARIOUS

1/3 * 3/3 does equal 1

When something takes the form of 1/3 it is defined as a finite number, therefore you can make the calculation.

In the form of a decimal, .333... is infinite, and as I said above, if you used the definition of infinity, you couldn't perform the calculation of .333... * 3 because in order to make the calculation you need a finite number.

.333... *3 == .999... !=1

 

[silverpig]

Originally posted by: Stefan

Originally posted by: MAME

Originally posted by: Stefan


This is stupid.

.333... * 3 != 1
.333... * 3 == .999...

For any practical purposes the answer is yes .999... = 1.
For any other reason, this is just a good way to waste time

LOL!!!!!!!!!!!!!!!!!!!!!!!!!!!

You honestly think .333... * 3 != 1? That's the dumbest thing I've ever heard.

so that means 1/3 * 3 = 3/3 != 1


HILARIOUS

1/3 * 3/3 does equal 1

When something takes the form of 1/3 it is defined as a finite number, therefore you can make the calculation.

In the form of a decimal, .333... is infinite, and as I said above, if you used the definition of infinity, you couldn't perform the calculation of .333... * 3 because in order to make the calculation you need a finite number.

.333... *3 == .999... !=1

0.3... is NOT infinite. If something is infinite then it is larger than x for all values of x. 0.3... is less than 4, therefore it is not infinite.

What about 1? It goes on forever. ...0001.000... yet you have no problems working with that number.

 

[DrPizza]

Originally posted by: Stefan

Originally posted by: MAME

Originally posted by: Stefan


This is stupid.

.333... * 3 != 1
.333... * 3 == .999...

For any practical purposes the answer is yes .999... = 1.
For any other reason, this is just a good way to waste time

LOL!!!!!!!!!!!!!!!!!!!!!!!!!!!

You honestly think .333... * 3 != 1? That's the dumbest thing I've ever heard.

so that means 1/3 * 3 = 3/3 != 1


HILARIOUS

1/3 * 3/3 does equal 1

When something takes the form of 1/3 it is defined as a finite number, therefore you can make the calculation.

In the form of a decimal, .333... is infinite, and as I said above, if you used the definition of infinity, you couldn't perform the calculation of .333... * 3 because in order to make the calculation you need a finite number.

.333... *3 == .999... !=1

*your* lack of ability to do the multiplication doesn't mean that those of us who have taken more math classes than you (or, as may be the case, got better grades in the same math classes) can't do the calculation. Multiplication of repeating decimals isn't difficult at all.

 

[Yzzim]

you guys have to have something better to do then argue about this ...

 

[BigToque]

Originally posted by: DrPizza

Originally posted by: Stefan

Originally posted by: MAME

Originally posted by: Stefan


This is stupid.

.333... * 3 != 1
.333... * 3 == .999...

For any practical purposes the answer is yes .999... = 1.
For any other reason, this is just a good way to waste time

LOL!!!!!!!!!!!!!!!!!!!!!!!!!!!

You honestly think .333... * 3 != 1? That's the dumbest thing I've ever heard.

so that means 1/3 * 3 = 3/3 != 1


HILARIOUS

1/3 * 3/3 does equal 1

When something takes the form of 1/3 it is defined as a finite number, therefore you can make the calculation.

In the form of a decimal, .333... is infinite, and as I said above, if you used the definition of infinity, you couldn't perform the calculation of .333... * 3 because in order to make the calculation you need a finite number.

.333... *3 == .999... !=1

*your* lack of ability to do the multiplication doesn't mean that those of us who have taken more math classes than you (or, as may be the case, got better grades in the same math classes) can't do the calculation. Multiplication of repeating decimals isn't difficult at all.

Grades are irrelevent to the question at hand. I am leaving the conversation as it stands. If you wish to think more highly of yourself because you *think* you have better grades than I in math classes that is fine by me.

As a change, you prove to me that .999... =1. I'm done attempting to prove that they are !=.

 

[MAME]

Originally posted by: Stefan
As a change, you prove to me that .999... =1. I'm done attempting to prove that they are !=.

OMFG, there's 2384982374 proofs posted about how they're equal and ZERO that state they're not equal.

Here's one, disprove plz:
http://mathforum.org/dr.math/faq/faq.0.9999.html

 

[silverpig]

Originally posted by: Stefan

Originally posted by: DrPizza

Originally posted by: Stefan

Originally posted by: MAME

Originally posted by: Stefan


This is stupid.

.333... * 3 != 1
.333... * 3 == .999...

For any practical purposes the answer is yes .999... = 1.
For any other reason, this is just a good way to waste time

LOL!!!!!!!!!!!!!!!!!!!!!!!!!!!

You honestly think .333... * 3 != 1? That's the dumbest thing I've ever heard.

so that means 1/3 * 3 = 3/3 != 1


HILARIOUS

1/3 * 3/3 does equal 1

When something takes the form of 1/3 it is defined as a finite number, therefore you can make the calculation.

In the form of a decimal, .333... is infinite, and as I said above, if you used the definition of infinity, you couldn't perform the calculation of .333... * 3 because in order to make the calculation you need a finite number.

.333... *3 == .999... !=1

*your* lack of ability to do the multiplication doesn't mean that those of us who have taken more math classes than you (or, as may be the case, got better grades in the same math classes) can't do the calculation. Multiplication of repeating decimals isn't difficult at all.

Grades are irrelevent to the question at hand. I am leaving the conversation as it stands. If you wish to think more highly of yourself because you *think* you have better grades than I in math classes that is fine by me.

As a change, you prove to me that .999... =1. I'm done attempting to prove that they are !=.

Read the goddam thread. There are a number of proofs in it.

 

[BigToque]

Originally posted by: silverpig

Originally posted by: Stefan

Originally posted by: DrPizza

Originally posted by: Stefan

Originally posted by: MAME

Originally posted by: Stefan


This is stupid.

.333... * 3 != 1
.333... * 3 == .999...

For any practical purposes the answer is yes .999... = 1.
For any other reason, this is just a good way to waste time

LOL!!!!!!!!!!!!!!!!!!!!!!!!!!!

You honestly think .333... * 3 != 1? That's the dumbest thing I've ever heard.

so that means 1/3 * 3 = 3/3 != 1


HILARIOUS

1/3 * 3/3 does equal 1

When something takes the form of 1/3 it is defined as a finite number, therefore you can make the calculation.

In the form of a decimal, .333... is infinite, and as I said above, if you used the definition of infinity, you couldn't perform the calculation of .333... * 3 because in order to make the calculation you need a finite number.

.333... *3 == .999... !=1

*your* lack of ability to do the multiplication doesn't mean that those of us who have taken more math classes than you (or, as may be the case, got better grades in the same math classes) can't do the calculation. Multiplication of repeating decimals isn't difficult at all.

Grades are irrelevent to the question at hand. I am leaving the conversation as it stands. If you wish to think more highly of yourself because you *think* you have better grades than I in math classes that is fine by me.

As a change, you prove to me that .999... =1. I'm done attempting to prove that they are !=.

Read the goddam thread. There are a number of proofs in it.

There isn't a god damn chance in hell I'm reading 1900+ posts

 

[DrPizza]

Originally posted by: Stefan
I am leaving the conversation as it stands. If you wish to think more highly of yourself because you *think* you have better grades than I in math classes that is fine by me.

As a change, you prove to me that .999... =1. I'm done attempting to prove that they are !=.

Well, that's all yours have been... attempting to prove they are !=. Unsuccessful attempts. You will never be successful though, because they ARE equal.
I can't say with certainty that I received higher grades than you in mathematics, but I could say with certainty that my grades >= your grades. (Plus, I majored in mathematics. You, obviously, did not, as this concept would be considered trivial in several of the upper level courses you would have taken.)

Nonetheless, numerous proofs have been presented throughout the first 1900 posts in this thread. RossGr provided the best I've seen in here. Care to place a wager on this? $100? (US funds) $200?

pdf with proofs, provided by RossGr

 

[DrPizza]

If you want to really stress your brain out, how about these:

1. Inside a 1x1 grid, does there exist a curve that is completely inside the grid, has 2 endpoints, yet has infinite length?
2. Do smooth curves exists inside such a square region, such that the curve will pass through *every* point in that region?
3. If the curve in (2) has infinite lenth, does it have to pass through all the points that the curve in (1) passes through?

Answer to the first two questions is yes, answer to the 3rd question is no.

 

[MAME]

Originally posted by: Stefan
There isn't a god damn chance in hell I'm reading 1900+ posts

then disprove the 2 posts with proofs that were just posted