.999~ = 1?

[One Winged Angel]

I feel like discussing some mathematics to get rid of all the stupid in this board.

So... can .999 repeating equal to 1?

[GameMaster]

Nope.

[Ginkasa]

It wouldn't equal one, no, but it would close enough that most people would just round up. The only reason I could see for not is if its part of some chemical equation or something that needs exact numbers.


*shrugs and walks away*

[DimHalo]

no it can't... if you analyze it with infinitive numbers it would never equal 1

[Yoda9864]

Well, no it isn't. But enjoy, if you will, a little play on concepts below:

.11111111111 repeating is 1/9 right?
.22222222222 repeating is 2/9 right?
so wouldn't .99999999 repeating be 9/9?
:sneaky:

[Vampyr]

Well, no it isn't. But enjoy, if you will, a little play on concepts below:

.11111111111 repeating is 1/9 right?
.22222222222 repeating is 2/9 right?
so wouldn't .99999999 repeating be 9/9?
:sneaky:

He knows too much. :minigun:

[gekko]

Well, no it isn't.

.11111111111 repeating is 1/9 right?
.22222222222 repeating is 2/9 right?
so wouldn't .99999999 repeating be 9/9?
:sneaky:

Yes, it is. There are numerous mathematical equations to prove it, you showed one. I've forgotten the others, and then I've seen some that are confusing as hell. But they all come back to prove that it's equal.

[gekko]

Nevermind, I remembered one.

Let n = .99~

10n = 9.99~

10n - n = 9, since the repeating decimals cancel out.

9n = 9, in other words, n = 1, but as we stated earlier, n = .99~. Conclusion: 1 = .99~

[One Winged Angel]

that was the exact equation I was about to post.. but this will work also.

1.000...
-.999...
_______
0

meaning... 1 = .999~

[GiMpY-wAnNaBe]

yep, exactly, and pi's exact value is 3

[Happydude]

yep, exactly, and pi's exact value is 3
thats a filthy lie and you know it!



as for .999~=1...it should but it doesn't

[Perfect Stu]

0.9~ = 1.0

I thought that was common knowledge? :confused:

[playa_playa]

Well, no it isn't. But enjoy, if you will, a little play on concepts below:

.11111111111 repeating is 1/9 right?
.22222222222 repeating is 2/9 right?
so wouldn't .99999999 repeating be 9/9?
:sneaky:

Well, no. Because in math, a number divided by itself will always be 1 (10!/10!=1 in the same way that 10^4/10^4=1). The only trouble is that .111~, for example, will never be expressed in full since its decimal points will be infinite. Therefore, repeating .999~ will never be a precise expression of 1. In other words. at any point you stop adding 9 to the end of the number, that number will deviate from an exact representation of 1. If you are being anal, 9x.99999999~ does not exactly equal 9, no matter how you slice it. It'll just be 8.99999~. It's just that as the numerator approaches the denomenator in value, the absolute value of the fraction itself will infinitely approach 1 - in this case, .999999~.

But this is all just a mathematical triviality, don't you guys think.

[GiMpY-wAnNaBe]

Well, no. Because in math, a number divided by itself will always be 1 (10!/10!=1 in the same way that 10^4/10^4=1). The only trouble is that .111~, for example, will never be expressed in full since its decimal points will be infinite. Therefore, repeating .999~ will never be a precise expression of 1. In other words. at any point you stop adding 9 to the end of the number, that number will deviate from an exact representation of 1. If you are being anal, 9x.99999999~ does not exactly equal 9, no matter how you slice it. It'll just be 8.99999~. It's just that as the numerator approaches the denomenator in value, the absolute value of the fraction itself will infinitely approach 1 - in this case, .999999~.

But this is all just a mathematical triviality, don't you guys think.
in that case, what is the difference between 1 and .9~ :p

[Rndm_Perfection]

.999 (repeating) IS equal to 1.


A repeating nine has an infinite height.

For two numbers to be different from one another, there must be a number that can fit between them.

Examples:
a) 1 and 2. 1.5 fits in between
b) 1.5 and 2. 1.7 fits in between
c) 1.0000000000001 and 1.00000000000011 ... even that has a number that fits in between. In fact, it has INFINITE numbers that fit in between.

There is absolutely no number that can fit between .9 repeating and 1.


Another way to look at it:

.9 repeating is the high end of the spectrum, being another term for "1". On the other end of the spectrum is .0 repeating. It's equal to zero, which most everyone should instantaneously agree to. However, there's a small number that would like to argue that since the zeros would progress into infinite, there could be an incomprehensable unit that would be similar to ".000(repeated)001" on paper, the 1 holding place for infinite.


Realize, folks, that infinite is not a number, but a term. As I said before, I hate infinite, but I do understand it.

And to those of you who said .99(repeated) is the largest number below 1, then .00(repeated) would have the be the smallest number above 0. Both of which are not true on a mathematical sense... which is the only sense for such a number O_o.

[Rndm_Perfection]

If you are being anal, 9x.99999999~ does not exactly equal 9, no matter how you slice it. It'll just be 8.99999~.

What're you talking about? 9.99 (repeated) multiplied by 9 would have to equal 9. How would you think otherwise? Did you use something like a calculator to check it? If so... I know that you did not press enough "9"s. If you even tried... you'd fail, for you'd die.

The point of multiplying the infinite ".99" is to not "slice" it, no matter what tool you're using.


To further explain...

9 x .9 is exactly .9 less than 9... which is 8.1
9 x 9.99 is exactly .09 less than 9... which is 8.81

If this continued "infinitely", then .999 repeating multiplied by 9 would have to be exactly .0(repeating) less than 9. And I assume you know .0(repeating) equals zero, and that you cannot tack a number (such as 9, in this instance) to the end of an infinite.

[playa_playa]

To further explain...

9 x .9 is exactly .9 less than 9... which is 8.1
9 x 9.99 is exactly .09 less than 9... which is 8.81

can you phrase this differently for the sake of clarity. 9 x 9.99 is 89.91, which is exactly .09 less than 90. Maybe you meant to say 9 x .999 is 8.991 which is exactly less than 9?

If this continued "infinitely", then .999 repeating multiplied by 9 would have to be exactly .0(repeating) less than 9. And I assume you know .0(repeating) equals zero, and that you cannot tack a number (such as 9, in this instance) to the end of an infinite.

The distinction of infinity is the difference. Your argument that there is no conceivable number between .999~ repeating and 1 is the clincher since a number cannot be tacked at the end of an infinite. Could there be a number to meet the infinitesimally receding value of the difference between .999~ and 1. Apparently not in a mathematical expression. So I'll admit I was wrong in an arithmetic sense. It's just a matter of grasping the concept of infinity (which I freely admit that I don't). But I keep thinking of a graph that infinitely approaches 1 as its limit.

[Jewels]

me confused and .999 is not equivalent to 1, it cant be

[Blackmane]

In terms of a limit, .999~ may come infinetely close to 1, breaking down the difference in an arithmatic sense. But, the fact remains that it is still less than one, and that makes a difference when you calculate it with respects to infinity.

[Dark Samurai]

uhhhh..... zuh???

brain hurtz

[Vampyr]

me confused and .999 is not equivalent to 1, it cant be

No, its not, but the problem is that you cant prove that its not.

[GiMpY-wAnNaBe]

it isn't equal...similar to how a hyperboly will never hit the axis...it comes infinitely close....but its never quite there

[Rndm_Perfection]

it isn't equal...similar to how a hyperboly will never hit the axis...it comes infinitely close....but its never quite there

That's all of your problems.

You're all thinking in terms of the foolish scientific theory... the theory that if someone aims to reach a destination, they will fail 100% of the time. Why, you ask? Because to get somewhere, you must travel half the distance... then half that distance... To get anywhere, you must infinitely travel half the distance. How does one manage to skip traveling half the distance? It's because infinite is irrelevant to real world applications. Infinite is a term.

A Hyperbola has limitations that this situation does not. A hyperbola gets infinitely close on purpose. A hyperbola that gets infinitely close to 1 does not cross .99(repeating), I guarantee it. A hyperbola not only gets infinitely close to a point, it also continues infinitely in a "parallel" direction (only parallel by appearance). Because it also continues infinitely and must infinitely get closer to the point... then there has to be space between the hyperbola and the line, no matter how small... so that it can get closer. In other words, since there is no number between .999(repeating) and 1 (as you can not put a number at the end of an infinite), then the point cannot feasably fit on the hyperbola, and therefor must also equal one.

I must emphasize once again that infinite is not a real number. It's applied a lot in mathematics, but it cannot be found on a number line.


If it cannot be understood that .99(repeated) is the same number as 1, then I will conclude any attempt of sensibility and leave it at the fact that this is merely a a gaming forum.

[Vampyr]

That's all of your problems.

You're all thinking in terms of the foolish scientific theory... the theory that if someone aims to reach a destination, they will fail 100% of the time. Why, you ask? Because to get somewhere, you must travel half the distance... then half that distance... To get anywhere, you must infinitely travel half the distance. How does one manage to skip traveling half the distance? It's because infinite is irrelevant to real world applications. Infinite is a term.

Scary. That made sense.

If it cannot be understood that .99(repeated) is the same number as 1, then I will conclude any attempt of sensibility and leave it at the fact that this is merely a a gaming forum.

Hmmm. You use the whole "This is merely a gaming forum" everytime a topic gets tricksy or out of control. :p

But, after much reviewing (and the fact that for some reason what Rndm said finally clicked and made sense...) I have concluded that .999~ is equal to 1. Because, as random has already pointed out, the difference between the two is .000~. Though it is hard to except, because we have been tought since 1st grade that decimals do NOT equal to a whole number...

I believe that the concept of .999~ = 1 is so hard to understand because it is virtually impossible for the human mind to concieve "infinity". No matter how hard you try, you can't really get the perfect idea of "infinite" into your head.

[Rndm_Perfection]

I believe that the concept of .999~ = 1 is so hard to understand because it is virtually impossible for the human mind to concieve "infinity". No matter how hard you try, you can't really get the perfect idea of "infinite" into your head.

Despite the fact that I sense fear in your tone (bwuahah), I am glad that you understood what I said. Congratulations. Comprehension feels good, doesn't it?

[Vampyr]

Despite the fact that I sense fear in your tone (bwuahah), I am glad that you understood what I said. Congratulations. Comprehension feels good, doesn't it?

I fear infinity. :sneaky:

Indeed comprehension is good, but it is still hard to believe that .999~ actually equals 1.

Im going to use the knowledge I have obtained in this thread to try to score some bonus points in my AP Probability Class, or in my Pre-Calc class I take next semester.

[Rndm_Perfection]

Im going to use the knowledge I have obtained in this thread to try to score some bonus points in my AP Probability Class, or in my Pre-Calc class I take next semester.

Sweet... good plan. Hey, if you need more knowledge about the evil known as infinite, you know where you can attempt to find it.

Bwuahah...


*shudders*
I feel like a little hermit in a cave who is hiding from unnecessary knowledge and fears... With my, I hold the weapon to destroy it, but I fear its power... aaaaah!

Ignore that last paragraph if you value your and my sanity.

[Vampyr]

Sweet... good plan. Hey, if you need more knowledge about the evil known as infinite, you know where you can attempt to find it.

Bwuahah...


*shudders*
I feel like a little hermit in a cave who is hiding from unnecessary knowledge and fears... With my, I hold the weapon to destroy it, but I fear its power... aaaaah!

Ignore that last paragraph if you value your and my sanity.

Your supposed to give us warnings like that BEFORE we read it. *shakes head*

And I'll try to get bonus points with what I know, and if that doesnt work, I'll need to come get some more to baffle my teacher with. :D

[ZebraRampage]

My math class is already hard enough...and now I'm on vacation. I don't feel like thinking about stuff like this...it seriously is making my brain hurt, not to mention that I just woke up.

[Bube]

But it's not just .9999999999..... Anything ending with .9999999999.... would equal the next number (that didn't make sense). Example:
3.99999999999....=4
9.99999999999....=10
2756.99999999....=2757

[Rndm_Perfection]

But it's not just .9999999999..... Anything ending with .9999999999.... would equal the next number (that didn't make sense). Example:
3.99999999999....=4
9.99999999999....=10
2756.99999999....=2757

That's true, because .99(repeated) is equal to one. Therefor 3 + .99(repeated) or... 3.999(repeated) must be equal to 4 (like 3 + 1)

[DimHalo]

*bored* but no one cares *leaves*

[GiMpY-wAnNaBe]

*bored* but no one cares *leaves*
HEY!!!!1

just because your not scientmatithic like the rest of us, doesn't mean that....you...ummm....go away :p

[Rndm_Perfection]

*bored* but no one cares *leaves*

With posts like that, I'm surprised you haven't met 1000 yet :p

[DimHalo]

With posts like that, I'm surprised you haven't met 1000 yet :p
precisely... why do you think i started posting like that? ... nah, i just didn't have much to do at the time... and i actually am scientmatithic (went to a science and math high school and am a math minor in college) ... just thought it was funny...you'll no longer see posts like that if it upsets you that much LOL

[Rndm_Perfection]

precisely... why do you think i started posting like that? ... nah, i just didn't have much to do at the time... and i actually am scientmatithic (went to a science and math high school and am a math minor in college) ... just thought it was funny...you'll no longer see posts like that if it upsets you that much LOL

Go right ahead, it adds "flavor"

[DimHalo]

Go right ahead, it adds "flavor"
well in that case.... nah, can't think of anything good...

was that enough "flavor"? :offtopic:

[GiMpY-wAnNaBe]

I know its looked down upon to revive old threads, but we just did this today in math, so i thought i'd bring up my now EDUCATED opinions


now, for the people who said it WASN'T equal, than you are admitting its impossible to move. You are also therefore admitting i am capable of beating ANY athlete in the world at any race, no matter the length, as long as i have a head start of ANY distance, regardless of the length of the race. I'll explain both of those in a second in a second.

now for the people who said it WAS equal, congratulations, your right, for a number of points that you already posted, also because if this, Between ANY two numbers, there has to be a number in between, If you can find me a number between .9 repeating and 1, well....go have a conversation with steven hawkings.

Now, for the impossibility of motion theory, think of it this way:

you want to run this length:

-------------------------------
but to run that length, you'd have to run half that:
----------------
and then half that:
--------
and then half that:
----
and then half that:
--
and then half that:
-
and then half that, and half that, and half that, and half taht, now, this is VERY similar to .9 repeating, well, actually if you take an infinate number of steps, you are at .9 repeating, and if this was not equal to 1, well you'd have a hard time getting where you want to go.


now about that race between me and top atletes, take Donaven Baily for example, championship runner for Canada a few years ago, now, me being a fairly bad runner, is, say, 10x slower than him. Now consider this, if i have a 100 metre head start:

in the time he runs the one hundred metres, i would run ten metres, now in the time that he ran the next ten metres, i'd run one metre, in the time that he ran that one metre, i'd be .1 metres ahead of him, in the time that he had run that .1 metres, i'd be .01 metres ahead, so therefore he can never reach me. I'd be glad to take anyone one of you on a bet that i cannot beat Donaven....really....i need the cash :D

but, ya, there you have two solid proofs that .99999999999999999999999999999 repeating = 1

[Rndm_Perfection]

Good stuff, but I covered all that before in this thread ¦¬Þ

[GiMpY-wAnNaBe]

lol......well.....shut up! :p