Poll: 0.999... = 1

[quhouv vhqwiufv qwiu]

The purpose of this thread is to assess how people react to counter-intuitive math. Basically, do you agree that 0.999... = 1, that is 0.9 reoccurring is equal to 1. I will post a proof after a few replies, but other people are free to post proofs before that.

EDIT: It says poll in the title but there is no poll :|.

 

[havass]

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...

 

[Rawle Lucas]

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 odd thing is that your proof is correct.

 

[crudus]

There is a pretty standard proof for it. I can't remember what it was because I wasn't a math major in college and I had it explained to me once. I found Graham's number more mind blowing that .9999... being equal to one.

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...

Every math major I have talked to and showed that to has described that as "shady".

 

[ExaltedK9]

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...

You just created a black hole. Only Chuck Norris can save us now!

 

[Nouw]

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...

Doesn't that imply 9x=10/x?

 

[Fanta Grape]

Learnt that in high school... Erm... Yeah

 

[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

 

[crudus]

Doesn't that imply 9x=10/x?

No because you did your algebra wrong. 9.99999999 isn't 9x it is 9+x.

 

[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.

 

[Naheal]

There is a pretty standard proof for it. I can't remember what it was because I wasn't a math major in college and I had it explained to me once. I found Graham's number more mind blowing that .9999... being equal to one.

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...

Every math major I have talked to and showed that to has described that as "shady".

Whenever someone puts that up to me, I point to this shirt:

 

[havass]

Every math major I have talked to and showed that to has described that as "shady".

I myself have my doubts about it, but I just can't find anything wrong in any step of the proof! Every step is perfectly logical.

 

[Nouw]

Doesn't that imply 9x=10/x?

No because you did your algebra wrong. 9.99999999 isn't 9x it is 9+x.

Not too good at Algebra you see. But somehow, it was the beginning of me unlocking my true math 'potential.'

Studying helps guys! And I know I'm asking for I don't know at least 5 people yelling their head off saying 'I didn't study and beat those who did.' That's being a dick by the way...

 

[Rubashov]

Well, 0.999... is equivalent to the infinite series .9 + .09 + .009 + .0009 + ..., which can be expressed as summation(9(.1^n)) from n = 1 to infinity, which is a geometric series of the form summation(a(r^n)) from n = 1 to infinity. Since geometric series converge to (ar)/(1-r) for |r| < 1, this series converges to (9(.1))/(1-.1) = (.9)/(.9) = 1. So yes, 0.999... is indeed equivalent to 1.

 

[Luftwaffles]

Yeah i do. Anyone who works in retail will see it that way. $5.99!!!! SALE ZOMG!

 

[crudus]

Whenever someone puts that up to me, I point to this shirt:

Spoiler

It's funny because that shirt divided by 0.

 

[quhouv vhqwiufv qwiu]

Every math major I have talked to and showed that to has described that as "shady".

I myself have my doubts about it, but I just can't find anything wrong in any step of the proof! Every step is perfectly logical.

There is an even simpler proof.

1/3 = 0.333...

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

But 0.333... + 0.333... + 0.333 = 0.999...

Hence 0.999 = 1

 

[Et3rnalLegend64]

Do we have to post proofs too? I agree that 0.99999=1 because I'm lazy and it's close enough (and it's actually really simple math to me so long as you stick to algebra). I was never a math person anyway. I preferred English grammar, comprehension, and spelling. It made it easy to constantly explain papers to my not-as-good-at-English dad or brother (the former is not a native speaker and the latter just doesn't click with vocab or spelling)

 

[Naheal]

Whenever someone puts that up to me, I point to this shirt:

Spoiler

It's funny because that shirt divided by 0.

Actually, it didn't :-/ That proof works.

Removed. Math major was doing drunk deriving.

 

[FalloutJack]

You know, I'm not sure that makes true logical sense. The thing here is that you have 0.9999... and one, and math decides it need to jump through some hoops to say that they equal each other. Well, in the strict sense, it is CLOSE ENOUGH to consider it that, but every unyielding calculator in the world says you're wrong, because they don't think in terms of 'close enough'. They think in terms of 1 = 1. Inventing a whole set of equations to prove that curve that never really touches 1 IS actually 1 is essentially like continuing to count towards infinity in the hopes of actually getting there, which you can't.