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Forums - General Discussion - Does 0.999... Equal 1?

Frodaddyg on 24 September 2008

Here we go:

.9 = 1 - 1/10^1
.99 = 1 - 1/10^2
.999 = 1 - 1/10^3

So, if you take that pattern out to infinity:

.999... = 1- 1/10^(infinity)

By definition, 10^(infinity) = infinity.

.999 - 1 - 1/(infinity)

The general definition is, anything divided by infinity = 0

So, .999... = 1 - 0

So, .999... = 1



The dedication you show to any particular console or company is inversely proportional to the number of times you have gotten laid. If you get laid enough, even if you prefer a certain brand, you just don't give enough of a shit to argue about it on the internet.

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Menago KF on 24 September 2008
vlad321 said:
Menago KF said:
steven787 said:
vlad321 said:

So here it goes, I hope this is not a joke thread because I'm about to waste 3 minutes of my life writing this up. From here on out S is sigma

0.999999 can be represented as the infinite sum of S(9 * (1/10) ^n) where n = 1 to infinity.This is basically sayying that 0.99999... = 9/10 +9/100 +9/1000 +....

Meanwhile the sum of a geometric series is PROVEN to be equal to :

a/(1-(1/r))

Where a is the first term, 0.9 in this case, and r is the rate of growth, 1/10 in this case. So where does that leave us?

0.9/(1-(1/10) =

= 0.9/( 9/10) =

= 0.9/0.9 =

= 1

 

 

And that is the easiest and way to prove this. The whole 0.3333 = 1/3rd is crap and not a real proof by any stretch of the imagination.

"n" is a theoretical number, so the proof is invalid.

It's a theoretical number, but one that exists in reality, that belongs to the so called "reality numbers".It can range from one to any postive number known that is not a fracture,or anything as strange (don't have the vocab to say what i want, but you understand i hope). His equation is valid.

 

You mean complex, as in it includes sqrt(-1)?

Anyways, there are a lot more theoretical things than will blow your mind than a simple sigma notation statement. Did you know that some infinities are greater than others? While the real numbers are infinite, the numbers which are not whole are more numerous than the reals?

The question of infinity was put to rest when Newton came along with his epsilon-delta definition.

 

 

I learned about it in my 3 year of high school, such things as infinity - and infinity +, where one infinity begins on the chart and does the other end before the first. It was quite fun. But that was in high school and my first year at Uni. Now i'm just learning simple urban planning/managment.



Huh. Who would've thought that beggining anew in my real life would coincide with starting anew on vgchartz?

Any day now, the dollar will be worth less than 2 zloty......any day now.....and my life savings will be in total jepordy ;(.

vlad321 on 24 September 2008
Menago KF said:
vlad321 said:
Menago KF said:
steven787 said:
vlad321 said:

So here it goes, I hope this is not a joke thread because I'm about to waste 3 minutes of my life writing this up. From here on out S is sigma

0.999999 can be represented as the infinite sum of S(9 * (1/10) ^n) where n = 1 to infinity.This is basically sayying that 0.99999... = 9/10 +9/100 +9/1000 +....

Meanwhile the sum of a geometric series is PROVEN to be equal to :

a/(1-(1/r))

Where a is the first term, 0.9 in this case, and r is the rate of growth, 1/10 in this case. So where does that leave us?

0.9/(1-(1/10) =

= 0.9/( 9/10) =

= 0.9/0.9 =

= 1

 

 

And that is the easiest and way to prove this. The whole 0.3333 = 1/3rd is crap and not a real proof by any stretch of the imagination.

"n" is a theoretical number, so the proof is invalid.

It's a theoretical number, but one that exists in reality, that belongs to the so called "reality numbers".It can range from one to any postive number known that is not a fracture,or anything as strange (don't have the vocab to say what i want, but you understand i hope). His equation is valid.

 

You mean complex, as in it includes sqrt(-1)?

Anyways, there are a lot more theoretical things than will blow your mind than a simple sigma notation statement. Did you know that some infinities are greater than others? While the real numbers are infinite, the numbers which are not whole are more numerous than the reals?

The question of infinity was put to rest when Newton came along with his epsilon-delta definition.

 

 

I learned about it in my 3 year of high school, such things as infinity - and infinity +, where one infinity begins on the chart and does the other end before the first. It was quite fun. But that was in high school and my first year at Uni. Now i'm just learning simple urban planning/managment.

 

Sorry, just the first line was meant for you, the rest was aimed atsteven787. Only quoted you to try to help you out.



Tag(thx fkusumot) - "Yet again I completely fail to see your point..."

HD vs Wii, PC vs HD: http://www.vgchartz.com/forum/thread.php?id=93374

Why Regenerating Health is a crap game mechanic: http://gamrconnect.vgchartz.com/post.php?id=3986420

gamrReview's broken review scores: http://gamrconnect.vgchartz.com/post.php?id=4170835

 

Menago KF on 24 September 2008
steven787 said:
Menago, I understand.

It really comes down to this.

If we want to use the representation of .(3) = 1/3, then
.(3) + .(3) + .(3) = 1 and not .(9)

It can't be both. In the real world a number can't have two values.

We have to pick the set of rules ahead of time (in this case: .(3) = 1/3), and justify the rules with other rules (in this case, the value of n).

 

You hit the point and yet you miss it ;P.

.(3) +.(3) +.(3)= .(9)= 1  because .(9) is equal to 1. That's why there is no problem, now do you understand my point of view clearly? It's something that i've been taught in math class, so i'm going to be stubborn about this :D



Huh. Who would've thought that beggining anew in my real life would coincide with starting anew on vgchartz?

Any day now, the dollar will be worth less than 2 zloty......any day now.....and my life savings will be in total jepordy ;(.

steven787 on 24 September 2008

I've understood it the whole time, I disagree. There are proofs for and against depending on what you are using the math for.

I just picked the minority side and started fighting. I have to go for a while, I'll check back in a couple of hours.



I would cite regulation, but I know you will simply ignore it.

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Menago KF on 24 September 2008

I'm sticking with my math classes. If you can't trust math taught in a former soviet country, where can you?



Huh. Who would've thought that beggining anew in my real life would coincide with starting anew on vgchartz?

Any day now, the dollar will be worth less than 2 zloty......any day now.....and my life savings will be in total jepordy ;(.

vlad321 on 24 September 2008
Menago KF said:
I'm sticking with my math classes. If you can't trust math taught in a former soviet country, where can you?

 

Amen!



Tag(thx fkusumot) - "Yet again I completely fail to see your point..."

HD vs Wii, PC vs HD: http://www.vgchartz.com/forum/thread.php?id=93374

Why Regenerating Health is a crap game mechanic: http://gamrconnect.vgchartz.com/post.php?id=3986420

gamrReview's broken review scores: http://gamrconnect.vgchartz.com/post.php?id=4170835

 

Rath on 24 September 2008
steven787 said:
Menago, I understand.

It really comes down to this.

If we want to use the representation of .(3) = 1/3, then
.(3) + .(3) + .(3) = 1 and not .(9)

It can't be both. In the real world a number can't have two values.

We have to pick the set of rules ahead of time (in this case: .(3) = 1/3), and justify the rules with other rules (in this case, the value of n).

It doesn't have two values, it has one value which can be represented in two different ways because 0.(9)=1.

 



Gnizmo on 24 September 2008

dtewi said:

It is easy. What is infity minus infinity? Zero! What is Infity times one infityth? One! Or alternatively, what is infinty divided by infity? One! What is infinity times 1? Infinty!

 

 Infinity divided by infinity is undefined in the same way 0/0 is undefined. I am pretty sure Infinity minus infinity is also undefined, but if it isn't then the answer is actually infinity. Infinity * 1/infinity is also undefined.  Infinity does not behave like real numbers that you are used to dealing with.

 To give you a bit of an idea of how quircky it is I will use the example my first Calculus teacher used. 1 is as close to infinity as 1 trillion, or -1 trillion. Infinity cannot be larger or smaller than what it is. Nothing you do to it can change its value. This is a bit simplified but I don't feel like getting my old text books out to go into greater detail.

 On topic: This is actually the subject of some debte amongst mathematicians I seem to recall. There is no decisive arguement for or against it. The only time it is ever going to be relevant though you will be using fractions anyways so it is kind of a moot point. You will never see .3 repeating *3 because it is drilled into your head with unrelenting force that decimals are too inaccurate to use until the absolute end of the equation.



Starcraft 2 ID: Gnizmo 229

Dgc1808 on 24 September 2008

No. It's a smaller value......

Unless were talking something like electronics were if something is said to run at 1V it actually runs at anything between 1.1 and 0.9, since nothing ever runs at an exact voltage.....



4 ≈ One