.999~ = 1?

GameMaster · 12-21-2003, 11:13 PM

Nope.

Ginkasa · 12-21-2003, 11:39 PM

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 · 12-22-2003, 12:16 AM

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

Yoda9864 · 12-22-2003, 12:34 AM

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?

Vampyr · 12-22-2003, 12:39 AM

Quote:

Originally Posted by 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?

He knows too much.

gekko · 12-22-2003, 12:58 AM

Quote:

Originally Posted by Yoda9864

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?

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 · 12-22-2003, 01:03 AM

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 · 12-22-2003, 01:16 AM

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

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

meaning... 1 = .999~

playa_playa · 12-22-2003, 02:37 PM

Quote:

Originally Posted by 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?

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 · 12-22-2003, 03:39 PM

Quote:

Originally Posted by playa_playa

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~

Rndm_Perfection · 12-23-2003, 12:50 AM

.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 · 12-23-2003, 12:59 AM

Quote:

Originally Posted by playa_playa

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 · 12-23-2003, 02:55 AM

Quote:

Originally Posted by Rndm_Perfection

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?

Quote:

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.