.9 repeated = 1?

**Flip** · Sep 7th, 2002, 11:01 PM

Does .9 repeated = 1? Here's the logic:

1/9 = .1 repeated
2/9 = .2 repeated
3/9 = .3 repeated

...

8/9 = .8 repeated
9/9 = ?

everything from 1-8 over nine = that number repeated. So when you get to 9/9 (1), it should be .9 repeated, assuming the pattern continues.

So what's up with this? .9 repeated CANNOT equal 1, but does the pattern just magicaly dissapear?

**SteveCRM** · Sep 7th, 2002, 11:14 PM

do a search....this debates already gone on

**NotLKH** · Sep 8th, 2002, 05:32 AM

Originally posted by Flip
.9 repeated CANNOT equal 1

Here we go again...

**marnitzg** · Sep 8th, 2002, 06:21 AM

YES! My legacy lives on

http://maya.effectonline.com/~vbforu...ghlight=.99999

**SilverSprite** · Sep 8th, 2002, 04:19 PM

What flip said earlier was pretty cool!

**NotLKH** · Sep 8th, 2002, 07:14 PM

Originally posted by SilverSprite
What flip said earlier was pretty cool!

Thats extremely interesting, but I tend to disagree since it seems to amount to a limited viewpoint upon the reality of the situation.
But, Mr. Sprite, I can see how you would think that such statements are pretty cool, with your track record.

just taking the piss outa you

**SilverSprite** · Sep 8th, 2002, 07:18 PM

Ouch NotLKH! I'm sorry if i'm not a 4 time university graduate like you guys. I'm only 15. I just happen to think it interesting.

And you still havent told me what you meant about the similar triangles in the winding function thread.

**SilverSprite** · Sep 12th, 2002, 04:53 PM

Hey NotLKH! How old are you? Do you go to school? And if you do where?

**bugzpodder** · Sep 12th, 2002, 05:20 PM

lol, what winding function thread?

**DiGiTaIErRoR** · Sep 13th, 2002, 03:01 AM

9/9 = 1

Moron.

**DiGiTaIErRoR** · Sep 13th, 2002, 03:24 AM

From that page:

Prove that 0.9999(recuring) = 1

Here goes:
let x = 0.9999(recuring)
then 10x = 9.9999(recuring)
then 10x-x = 9.9999(recuring) - x
then 9x = 9
then x = 1

Well....?

Infinity is an idea, repeated 9's would be an infinty. Infinity cannot be expressed as a number.

x=.9
10x=9
10x-x=9-.9
9x=8.1
x=.9

Your flaw is this there is no such thing as infinity, when multiplied by 10 the length of the numbers would remain constant, like .9999 becomes 9.999. Where as you'd have .9999 = 9.9999. You are inventing numbers. This is unaccurate(ever hear of significant digits?). As such your result is not accurate.

It's as simple as that. You're wrong. Precise, sure! Accurate? Nope!

x=.9
10x=9.9
10x-x=9.9-.9
9x=9
x=1

When I invent numbers I can make it = 1 too.

x=.9
10x=9.99
10x-x=9.99-.9
9x=9.09
x=1.01

I can also make it greater than 1. I'm not accurate, but I'm precise.

**Evil_Giraffe** · Sep 13th, 2002, 05:31 AM

Yeah, except .(9) * 10 = 9.(9) whereas .9 * 10 != 9.9 or 9.99

Infinity is not a number, therefore when you have an infinite number of digits you can't use the standard rules, which are a special case of mathematical laws for when there are a finite number of digits. You can't have "1 less than infinity" number of digits precisely because infinity is not a number.

And "there is no such thing as infinity". Wow. The ignorance there is unbelievable.

**DiGiTaIErRoR** · Sep 13th, 2002, 12:41 PM

By that I meant infinity is simply an idea, it is not applicable to reality.

There is nothing in this universe which is infinite except space. Space being the vacum of our universe.

Everything in life is finite. In no case would you have .9999... recuring for ever, that is an accuracy which is impossible.

So, while the solution is technically correct, the applicability of it is irrelevent.

Unless you can have absolute infinite accuracy. Which is an oxymoron.

**A$$Bandit** · Sep 13th, 2002, 01:18 PM

An arguement for the equivalence of 1 and 0.9 recurring is as someone said:

Here goes:
let x = 0.9999(recuring)
then 10x = 9.9999(recuring)
then 10x-x = 9.9999(recuring) - x
then 9x = 9
then x = 1

A more shifty little argument though:

Given a positive real number x, find the positive square root of it (calling the positive square root Root(x)). Examining the behavior of Root(x) with different groups of values for x, it seems that:
If x > 1, Root(x) > x > 1
If x = 1, Root(x) = x = 1
If x < 1, Root(x) < x < 1

Now let's say that Root(x) = 0.9 recurring. It's pretty safe to say that x < 0.9 recurring, but we just defined x as being between Root(x) and 1, therefore:
0.9 recurring < x < 1

This pretty much proves that 0.9 recurring = 1.

**bugzpodder** · Sep 13th, 2002, 02:51 PM

Originally posted by DiGiTaIErRoR
9/9 = 1

Moron.

Moron? you got some guts coming here and calling other people morons! apparently, after reading your post, i think the moron here is you. I guess pi and e will no longer have infinite amount of decimals, its gotta be terminating right?

1/3 no longer becomes 0.33333..., because according to you there is no infinity, so 1/3 actually = 0.333...3333

LOOK AT WHAT YOU ARE SAYING!!!!!!!

**SilverSprite** · Sep 13th, 2002, 03:28 PM

pfft and he calls himself a mathematician!lol(joking around)

**Kalkewl8ter** · Sep 13th, 2002, 03:58 PM

Infinity is an idea, which only means it is NOT a number.
However, it CAN be used when working with numbers.
0.9 repeating=1
It's a known fact.
Live with it.

**SilverSprite** · Sep 13th, 2002, 04:20 PM

YA! BELY DAT!lol

**DiGiTaIErRoR** · Sep 14th, 2002, 01:54 PM

.9 repating may be similar to 1 but it is not one.

There is no real-world application where .9 repeating can exist. It would be infinite accuracy, there's no such thing. All real-world measures will terminate, if you go far enough.

So in the real-world .9 repeating != 1. Maybe in Happy Land on Lolli-pop Lane .9 repeating will = 1.

Consider this, what would you add to .9 repeating to get 1? By your definition it would be 0. It would really be .0 repeating then a 1, but can you define a 1 after infinite 0's? Oh yeah! That infinity plus one stuff you used to use when arguing with your sibblings.

x=.0...1
y=.999...
x+y=1
10x=.0...1
10x-x= .0...1-.0...1
9x=0
x=0
x+y=.999...

**bugzpodder** · Sep 14th, 2002, 02:01 PM

so mr digitalerror here claims there there is an end to inifinity as he added a 1 in the end of the infinite 0s to get 0.000...1

so apparently he recognizes inifinity as a finite number. does anyone want to tell him whats wrong with that?

and yet strangely, he himself proved that x+y=1=0.999...

...

**SilverSprite** · Sep 14th, 2002, 02:02 PM

I do! Mr. DigitalError, your wrong with that!

**DiGiTaIErRoR** · Sep 14th, 2002, 02:04 PM

I'm just pointing out the error in .999=1.

**SilverSprite** · Sep 14th, 2002, 02:06 PM

Your right about one thing. .999 doesnt = 1. but .9(recurring)does!

**DiGiTaIErRoR** · Sep 14th, 2002, 02:07 PM

In fantasy land.

**SilverSprite** · Sep 14th, 2002, 02:09 PM

Maybe you've got things in reverse. This is the real life, not 'fantasy land'. And that place in your head, thats fantasy land.

**DiGiTaIErRoR** · Sep 14th, 2002, 02:17 PM

.999... recuring is not a 'real' number. It can only be imagined.

**SilverSprite** · Sep 14th, 2002, 04:37 PM

ok and.... therefore it equals 1

**DiGiTaIErRoR** · Sep 14th, 2002, 05:34 PM

it does not equal 1, it is similar to 1

you cannot have a real number = infinity

.999... repeating is like saying .9*infinity

1*infinity=27*infinity

By your logic I can eliminate infinity.

so 1=27

as 9.999... - .999... you're basicly subtracting infinity from infinity. Since repeating 9's cannot be expressed, as infinity. Repeating 9's is an idea, like infinity.

So .999 <> 1. If you believe so you're a moron.

**SilverSprite** · Sep 14th, 2002, 05:40 PM

what in the name of hell is 27*infinity? That has nothing to do with .9(recurring). Your saying that 27*infinity is the same as .9*infinity? The only moron here is you. Who comes into a forum calling people morons? Since youve started it i'm gonna call you one too. YA MORON

**DiGiTaIErRoR** · Sep 14th, 2002, 05:44 PM

Express .9 repeating as a real number.

**SilverSprite** · Sep 14th, 2002, 05:46 PM

I have nothing more to say to you. I dont talk to moronic people like you! MORON!(9/9)

**DiGiTaIErRoR** · Sep 14th, 2002, 05:46 PM

You're the moron. You can't prove me wrong.

**SilverSprite** · Sep 14th, 2002, 05:48 PM

Shut up Moron!

**DiGiTaIErRoR** · Sep 14th, 2002, 05:49 PM

Have you ever heard of checking your solution?

let x = 0.9999(recuring)
then 10x = 9.9999(recuring)
then 10x-x = 9.9999(recuring) - x
then 9x = 9
then x = 1

put your x back in the original equation

1=.9999(recuring)

The solution doesn't check therefore 1 is not in the solution set of x.

Moron.

**SilverSprite** · Sep 14th, 2002, 05:50 PM

I dont talk to morons. I will have nothing more to do with you!!!MORON MORON MORON thats infinite

**DiGiTaIErRoR** · Sep 14th, 2002, 05:51 PM

Just like I an have:

let x=2
then x^2=4
then -2^2=4
so x=-2

therefore 2=-2

I can be a moron like you too!

**bugzpodder** · Sep 14th, 2002, 06:07 PM

right "0.999... doesn't exist you can't prove me wrong!" whats your reason? infinite accuracy doesn't exist?

well newsflash, it does. if you are in a room with 5 other people, you'd say that there are EXACTLY 6 people in the room, and the number 6 is INFINITELY ACCURATE. --- we can't have 5 and 3/4 people, we can't have 6 and 1/7 people! and apprently you think infinity doesn't exist! let me ask you something, what is infinity?

do you even know what you talk about before you say it?? I've had it with you and your attitude. I see that the biggest moron here is you!

**DiGiTaIErRoR** · Sep 14th, 2002, 07:22 PM

You're confusing infinite with absolute.

**bugzpodder** · Sep 14th, 2002, 07:26 PM

an absolute value has infinite accuracy.

**Kalkewl8ter** · Sep 14th, 2002, 07:37 PM

DigitalError previously stated the following:

Have you ever heard of checking your solution?

let x = 0.9999(recuring)
then 10x = 9.9999(recuring)
then 10x-x = 9.9999(recuring) - x
then 9x = 9
then x = 1

put your x back in the original equation

1=.9999(recuring)

The solution doesn't check therefore 1 is not in the solution set of x.

However, the final conclusion that 1 is not in the solution set of x is false. There is no proof that 1 cannot=0.9 recurring, which means that you cannot put in the last statement and claim it valid. It is simply your word against ours, except for that fact that we have proof and you don't.

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