Is 1 = 0.9999......

[CrazyPerson]

oh no... this is back

 

[TuxDave]

Originally posted by: TravisT
This is not true..... .9999999 does not equal 1

Even in a real life scenario. If you shoot a rocket to the moon, or better yet, pluto. The angle of your rocket is set at 1... you fire the rocket and it hits pluto. Then you reset the rocket at an angle of .999999999 (When in real life you can not set an infinite, however, you would have to stop somewhere.... Your rocket may still hit but it would be a significant difference from the first one fired. No?

Ah ha... but the argument stands that if we were to set it to an angle of 0.9999.... we may as well set it at 1 because they are theoretically equal.

 

[MovingTarget]

Yes, this thread...older than the internet itself. Are we trying for some sort of record here?

Ok, now for my .02 1 !=0.99999999.... However, it does approach 1. And no, I dont feel like posting that limit because its most likely posted within the first two pages of this thread. Have fun looking for it!

 

[MAME]

They are exactly equal

 

[ElFenix]

Originally posted by: MovingTarget
Yes, this thread...older than the internet itself. Are we trying for some sort of record here?

Ok, now for my .02 1 !=0.99999999.... However, it does approach 1. And no, I dont feel like posting that limit because its most likely posted within the first two pages of this thread. Have fun looking for it!

no... women vs computers is older than the internet itself

 

[RossGr]

Originally posted by: MovingTarget
Yes, this thread...older than the internet itself. Are we trying for some sort of record here?

Ok, now for my .02 1 !=0.99999999.... However, it does approach 1. And no, I dont feel like posting that limit because its most likely posted within the first two pages of this thread. Have fun looking for it!

A fixed number cannot "approach" anything, it is fixed after all. If .999.... is not fixed it is not a number. So now you need to think about it abit, and try to explain to yourself how a one fixed number can approach another? They are either equal or they are not. It so happens that .999.... is every bit as fixed as .333.... or .5 or any other decimal number. It does not approach 1 it IS 1.

 

[MAME]

Well said RossGr

 

[FrustratedUser]

Wow

 

[DrPizza]

Yes, for the 20th time I've posted it.... .99999........ EQUALS EXACTLY 1

For those who think it's not, let me point out that intuition is NOT mathematical proof. There is no mathematical proof otherwise, but there are many proofs that they are equal. However, if any of you Einstein's think you have proven that .9999....repeating DOESN'T equal 1 exactly, why don't you get your proof published and become world famous? You'd probably win the award in math that's equivalent to the Nobel prize (damn that Nobel... didn't he think math was important enough?)

 

[DrPizza]

Yes, for the 20th time I've posted it.... .99999........ EQUALS EXACTLY 1

For those who think it's not, let me point out that intuition is NOT mathematical proof. There is no mathematical proof otherwise, but there are many proofs that they are equal. However, if any of you Einstein's think you have proven that .9999....repeating DOESN'T equal 1 exactly, why don't you get your proof published and become world famous? You'd probably win the award in math that's equivalent to the Nobel prize (damn that Nobel... didn't he think math was important enough?)

 

[silverpig]

20th and 21st now

 

[crazygal]

I had a meeting with Bill Barnier, a Math Professor at Sonoma State University. He has a PhD (Algebraic Topology), 1967, UCLA. He teaches many of the upper division courses and is considered one of the smartest teachers here. He has won various awards, including two within the last few months. He also wrote a textbook for Discrete Mathematics which is used in colleges all over the country. He also came up with a hyper-geometric equation used in probability with a colleague. Needless to say, he was a good choice to talk about the subject matter.

Although he was most helpful, I was unable to write all that I needed to explain the topic the best way possible. It?s not that crucial though, as the truth remains the same.

Most of this has been said in the other thread but I will write what I was told by a reliable source as to eliminate doubt.
To start, we?ll keep it simple:
Lets say m=.999?
Multiply both sides by 10 to get 10m = 9.999?
Subtract m from both sides to get 9m = 9
Divide and you find that m=1.
Although that is not a ?proof? per se, it is completely valid and is an easy way of seeing .999??s value.

Here?s a more in depth look:
.999? is an infinite series show here: 9/10 + 9/100 + 9/1000 + ?.
Factor out the 9/10 to get 9/10(1 + 1/10 + 1/100 + ?)
The rate of change inside the parenthesis is 1/10 (shown as r below). Since it?s less than one we know the formula converges and we can use an infinite sum equation. (Calc 2)
The equation then looks like this:
9/10(1/(1-r))
= 9/10(10/(10-1))
subtract and cancel and you?re left with 1.

Another way to look at the same formula is to assume you have a line from 0 to 1 and you?re going 9/10?s of the remaining distance to 1 each interval. Thus you get to 9/10 the first interval, then 99/100 on the second interval, then 999/1000?and so on.
If you take n intervals, you can represent this process with the same equation:
9/10[(1-(1/10)^n) / (1-(1/10))]
Since n goes to infinity, (1/10)^n equals 0.
Thus we?re left with the same as before;
9/10(1/(1-(1/10)) = 1

Finally, if you can agree that 1/3 = .333? (which it absolutely does),
Then we can multiply that by 3: 3(1/3) = 3(.333?)
Thus 1 = .999?
So if you believe that 1/3 = .333? then it is impossible for 1 != .999?

I know it?s hard to read, by try and write these equations on paper if you need to.

To sum it up, 1 is EXACTLY equal to .999? If you do not agree, please please please talk to a math professor who will sit down and work through it with you. It is not a topic up for debate in the math field because it?s a fact and has been proven. Please listen to the experts!

 

[Krugger]

Originally posted by: crazygal

To start, we?ll keep it simple:
Lets say m=.999?
Multiply both sides by 10 to get 10m = 9.999?
Subtract m from both sides to get 9m = 9
Divide and you find that m=1.
Although that is not a ?proof? per se, it is completely valid and is an easy way of seeing .999??s value.

Here?s a more in depth look:
.999? is an infinite series show here: 9/10 + 9/100 + 9/1000 + ?.
Factor out the 9/10 to get 9/10(1 + 1/10 + 1/100 + ?)
The rate of change inside the parenthesis is 1/10 (shown as r below). Since it?s less than one we know the formula converges and we can use an infinite sum equation. (Calc 2)
The equation then looks like this:
9/10(1/(1-r))
= 9/10(10/(10-1))
subtract and cancel and you?re left with 1.

Another way to look at the same formula is to assume you have a line from 0 to 1 and you?re going 9/10?s of the remaining distance to 1 each interval. Thus you get to 9/10 the first interval, then 99/100 on the second interval, then 999/1000?and so on.
If you take n intervals, you can represent this process with the same equation:
9/10[(1-(1/10)^n) / (1-(1/10))]
Since n goes to infinity, (1/10)^n equals 0.
Thus we?re left with the same as before;
9/10(1/(1-(1/10)) = 1

Finally, if you can agree that 1/3 = .333? (which it absolutely does),
Then we can multiply that by 3: 3(1/3) = 3(.333?)
Thus 1 = .999?
So if you believe that 1/3 = .333? then it is impossible for 1 != .999?

there's just one thing that bothers me here:
---
Lets say m=.999?
Multiply both sides by 10 to get 10m = 9.999?
Subtract m from both sides to get 9m = 9
---
you're stating that 10m - .9999.... is = to 9 in your proof, you can't do that. you can't use .9999.... = 1 in a proof to prove .9999.... = 1 that's faulty logic.
there are other parts that bother me too, but you're just gonna rely on what mathmatics has taught you to think. like that 1/3=.3333 so 1 must = .9999

and i swear next time i see john nash walkin around campus i'm gonna stop and ask him...

 

[MegaloManiaK]

Originally posted by: crazygal
I had a meeting with Bill Barnier, a Math Professor at Sonoma State University. He has a PhD (Algebraic Topology), 1967, UCLA. He teaches many of the upper division courses and is considered one of the smartest teachers here. He has won various awards, including two within the last few months. He also wrote a textbook for Discrete Mathematics which is used in colleges all over the country. He also came up with a hyper-geometric equation used in probability with a colleague. Needless to say, he was a good choice to talk about the subject matter.

Although he was most helpful, I was unable to write all that I needed to explain the topic the best way possible. It?s not that crucial though, as the truth remains the same.

Most of this has been said in the other thread but I will write what I was told by a reliable source as to eliminate doubt.
To start, we?ll keep it simple:
Lets say m=.999?
Multiply both sides by 10 to get 10m = 9.999?
Subtract m from both sides to get 9m = 9
Divide and you find that m=1.
Although that is not a ?proof? per se, it is completely valid and is an easy way of seeing .999??s value.

Here?s a more in depth look:
.999? is an infinite series show here: 9/10 + 9/100 + 9/1000 + ?.
Factor out the 9/10 to get 9/10(1 + 1/10 + 1/100 + ?)
The rate of change inside the parenthesis is 1/10 (shown as r below). Since it?s less than one we know the formula converges and we can use an infinite sum equation. (Calc 2)
The equation then looks like this:
9/10(1/(1-r))
= 9/10(10/(10-1))
subtract and cancel and you?re left with 1.

Another way to look at the same formula is to assume you have a line from 0 to 1 and you?re going 9/10?s of the remaining distance to 1 each interval. Thus you get to 9/10 the first interval, then 99/100 on the second interval, then 999/1000?and so on.
If you take n intervals, you can represent this process with the same equation:
9/10[(1-(1/10)^n) / (1-(1/10))]
Since n goes to infinity, (1/10)^n equals 0.
Thus we?re left with the same as before;
9/10(1/(1-(1/10)) = 1

Finally, if you can agree that 1/3 = .333? (which it absolutely does),
Then we can multiply that by 3: 3(1/3) = 3(.333?)
Thus 1 = .999?
So if you believe that 1/3 = .333? then it is impossible for 1 != .999?

I know it?s hard to read, by try and write these equations on paper if you need to.

To sum it up, 1 is EXACTLY equal to .999? If you do not agree, please please please talk to a math professor who will sit down and work through it with you. It is not a topic up for debate in the math field because it?s a fact and has been proven. Please listen to the experts!

Sorry im all out of cookies today.

 

[spidey07]

Yes krugger. All the smart math people that made a career out of it in the world are wrong.

 

[Splork]

I can't believe this post is still in debate.. essh!

-sp

 

[naddicott]

Originally posted by: spidey07Yes krugger. All the smart math people that made a career out of it in the world are wrong.

Read the thread. There are links to "smart math people" with PhDs making a career out of it and all that who argue otherwise (on more than just "instinct"). Nobody in this thread has ever gone to those links, read those arguments, and come back with a full refutation. Everyone just keeps coming back with the same tired "proofs" that have had holes poked in them around 300 times each, assuming they're the first ones to awe us with their ability to paraphrase pages they found with google.

If someone is really going to bother a math professor with this silly topic, at least print out the relevant articles and have them provide some counter to the deeper issues. Have them answer questions like "are we sure an addition/multiplication operation on a "0.X..." type number is even possible?'.

I gathered last time I looked into this that the real mathmatical debate behind this question is a matter of fundamental theory that we are trained to take on faith, but in truth we have no better raitionale for that faith than the fact that it's convenient. The trendy approaches towards such theories (specifically the nature of real numbers) is not static from decade to decade.

At current count - 50.56% ATers say 1 != 0.999..... That's about as much resolution on this issue as we're likely to get here.

 

[Turkish]

Originally posted by: crazygal
What in the hell....they are EXACTLY equal people!
Don't believe me? Go talk to a math professor.

^^^^ here is a genius :Q

 

[Kyteland]

Originally posted by: naddicott
At current count - 50.56% ATers say 1 != 0.999..... That's about as much resolution on this issue as we're likely to get here.

What I want to know is if I go and delete the "no, it isn't" option from the poll and then readd it, will all of those votes be lost? :evil:

I'm afraid of how many people I'd piss off if I tried it.

 

[MegaloManiaK]

Originally posted by: Kyteland

Originally posted by: naddicott
At current count - 50.56% ATers say 1 != 0.999..... That's about as much resolution on this issue as we're likely to get here.

What I want to know is if I go and delete the "no, it isn't" option from the poll and then readd it, will all of those votes be lost? :evil:

I'm afraid of how many people I'd piss off if I tried it.

Heh, i say do it, at least then the mods can lock this up so it doesn't get regurgitated (sp?) again in a month.

You know what they say about arguing on the internet and the special olympics.....

 

[crazygal]

there's just one thing that bothers me here:
you're stating that 10m - .9999.... is = to 9 in your proof, you can't do that

Perhaps you're missing something?
Here's what I wrote clairifed:
10m = 9.999...
subtract m from both sides:
10m - m = 9m (that's the left side)
and 9.999... - .999... = 9 (that's the right side).

An easier way to see it is to line them up like so:
9.999999...
- 0.999999...
-----------------
9

I did not violate anything.

 

[thraashman]

Originally posted by: crazygal

there's just one thing that bothers me here:
you're stating that 10m - .9999.... is = to 9 in your proof, you can't do that

Perhaps you're missing something?
Here's what I wrote clairifed:
10m = 9.999...
subtract m from both sides:
10m - m = 9m (that's the left side)
and 9.999... - .999... = 9 (that's the right side).

An easier way to see it is to line them up like so:
9.999999...
- 0.999999...
-----------------
9

I did not violate anything.

Actually you did violate something. 9.9999..... - 0.99999...... is technically undefined. As you cannot do set mathematical actions with infinites. Infinity minus infinity is not zero, it's still infinity. So you cannot perform the mathematical action of 9.9999...... - 0.9999.......

So 0.99999...... != 1, though they are logically equivalent, they are not equal.




And please let this thread DIE!!!!!!!!!!

 

[jman19]

Originally posted by: thraashman

Originally posted by: crazygal

there's just one thing that bothers me here:
you're stating that 10m - .9999.... is = to 9 in your proof, you can't do that

Perhaps you're missing something?
Here's what I wrote clairifed:
10m = 9.999...
subtract m from both sides:
10m - m = 9m (that's the left side)
and 9.999... - .999... = 9 (that's the right side).

An easier way to see it is to line them up like so:
9.999999...
- 0.999999...
-----------------
9

I did not violate anything.

Actually you did violate something. 9.9999..... - 0.99999...... is technically undefined. As you cannot do set mathematical actions with infinites. Infinity minus infinity is not zero, it's still infinity. So you cannot perform the mathematical action of 9.9999...... - 0.9999.......

So 0.99999...... != 1, though they are logically equivalent, they are not equal.




And please let this thread DIE!!!!!!!!!!

"mathematical action"

"...hough they are logically equivalent, they are not equal"

Wow, there are a lot of people in this thread that think they know what they're talking about, but really don't.

 

[RossGr]

Originally posted by: thraashman

Originally posted by: crazygal

there's just one thing that bothers me here:
you're stating that 10m - .9999.... is = to 9 in your proof, you can't do that

Perhaps you're missing something?
Here's what I wrote clairifed:
10m = 9.999...
subtract m from both sides:
10m - m = 9m (that's the left side)
and 9.999... - .999... = 9 (that's the right side).

An easier way to see it is to line them up like so:
9.999999...
- 0.999999...
-----------------
9

I did not violate anything.

Actually you did violate something. 9.9999..... - 0.99999...... is technically undefined. As you cannot do set mathematical actions with infinites. Infinity minus infinity is not zero, it's still infinity. So you cannot perform the mathematical action of 9.9999...... - 0.9999.......

So 0.99999...... != 1, though they are logically equivalent, they are not equal.




And please let this thread DIE!!!!!!!!!!

Really and neat argument... Trouble is this is not a proof, this is a demonstration. Now you need to address a real proof.

 

[Kyteland]

Originally posted by: thraashman

Actually you did violate something. 9.9999..... - 0.99999...... is technically undefined. As you cannot do set mathematical actions with infinites. Infinity minus infinity is not zero, it's still infinity. So you cannot perform the mathematical action of 9.9999...... - 0.9999.......

So 0.99999...... != 1, though they are logically equivalent, they are not equal.


And please let this thread DIE!!!!!!!!!!

I will now prove that you can do set mathematical actions with infinites using proof by contradiction:

Assume that you cannot do set mathematical actions with infinites
0.666..... is an infinite number (2/3)
0.166..... is an infinite number (1/6)

0.666... - 0.166... = .5

Since subtraction is a set mathematical action and I performed it successfully with infinites the hypothesis has been contradicted proving that you can do set mathematical actions with infinites.



And if you want the thread to die why don't you try NOT POSTING IN IT!!!!!!!!!!one