.9~=1

[Killer Tree]

~ = repeating


.999~=x
10x=9.999~
10x - x = 9x
9x=9
1x=1.
.999~ = 1.



A simpler but not shure if it is legal is.
1/3=.3~
1/3 X 3 = 3/3
3/3=1
.3~ X 3 = .9~
.9~ = 1



<___<

lolz Math'D

 

[leafgreen386]

Nice little trick there.

.999~=x
10x=9.999~
10x - x = 9x
9x=9
1x=1.
.999~ = 1.

Where do you get the nine from though?

 

[Doraki]

9x=10x-x=9.999~-0.999~=9

 

[Killer Tree]

.999~=x
10x=9.999~
10x - x = 9x
9x=9
By multiplying .99999999999999(which is x) by 10 I get 9.9999999999999 minus the x leaves 9

 

[leafgreen386]

lol trying to find an error in your math I made one myself

k I give up then. .999~=1

 

[sheepyman]

You're right, but you went about it the wrong way. You have to use limits. I can't make the proper symbols and writing isn't my favorite past time so you can either believe me or figure it out yourself; it's not too hard.

 

[Lefticle]

lol trying to find an error in your math I made one myself

k I give up then. .999~=1

Yeah, it has to, since .333~=1/3.

 

[Flamestar666]

Yeah, it has to, since .333~=1/3.

no, .999~=1

EDIT:here, i did the math


let x = 0.999999.... forever
then 10x = 9.9999999...... forever

then 10x = 9.99999.... minus x (0.99999....)
equals exactly 9

so 10x -x = 9x
and 10x-x = 9

so 9x = 9
x = 1

 

[Killer Tree]

no, .999~=1

EDIT:here, i did the math


let x = 0.999999.... forever
then 10x = 9.9999999...... forever

then 10x = 9.99999.... minus x (0.99999....)
equals exactly 9

so 10x -x = 9x
and 10x-x = 9

so 9x = 9
x = 1

He didn't say it was wrong.

 

[G.Fizzle]

O.k.a.y......

 

[Lefticle]

no, .999~=1

Yes, I know. I'm saying it can be easily figured out if you take into consideration that .333~=1/3.

(1/3)3=1
(.333~)3=.999~

 

[bornfidelity.com]

~ = repeating


.999~=x
10x=9.999~
10x - x = 9x
9x=9
1x=1.
.999~ = 1.



A simpler but not shure if it is legal is.
1/3=.3~
1/3 X 3 = 3/3
3/3=1
.3~ X 3 = .9~
.9~ = 1



<___<

lolz Math'D

This is mathematically correct, only because mathematically there's an end to infinity.
This is in real life incorrect, because in real life infinity is infinite.

 

[Killer Tree]

This is mathematically correct, only because mathematically there's an end to infinity.
This is in real life incorrect, because in real life infinity is infinite.

ummm no

There is no end to infinite mathmaticaly. By your logic it is right in real life and wrong mathematically.

 

[Doraki]

Bf.com, here's some piece of advice :
When something is true, well... guess what... *spoiler*

Spoiler

it IS true.

 

[GaNoNdOrFgUrL]

@_@................................nice job u just fried my brain.

 

[Doraki]

Killer Tree, time to go a bit further : what's 0.913749137491374~ equal to ?

 

[Rici]

.999~=x
10x=9.999~
10x - x = 9x
9x=9
1x=1.
.999~ = 1.

Where the **** did you get 9x=9?
10 x 0.999~= 9.99~0 (notice the 0 at the end.. 10 x 0.9= 9.0)
10 x 0.999~ - 0.999~= 9.99~0- 0.999~
this means that
9x= just a little less then 9
x= a little less then 1 = 0.999~

see where I'm going?
so your wrong.

Also, 1/3 can't be written in decimals. Even infinity is just to short for 1/3. So the second one is also wrong.

As far as I know, math has no errors, only some imperfections like you can't devide by 0.

 

[Wenbobular]

The 9x = 9 comes from10x = 9.999~
Since x is .999~ and 9.999~ - .999~ = 9, you can substitute it in for 10x - x = 9. Or something along those lines. I still find this proof weird though. *Shrug* stupid math. Hehe.

 

[Killer Tree]

10 x 0.999~= 9.99~0 (notice the 0 at the end.. 10 x 0.9= 9.0)
10 x 0.999~ - 0.999~= 9.99~0- 0.999~
this means that
9x= just a little less then 9
x= a little less then 1 = 0.999~

see where I'm going?
so your wrong.

Also, 1/3 can't be written in decimals. Even infinity is just to short for 1/3. So the second one is also wrong.

As far as I know, math has no errors, only some imperfections like you can't devide by 0.

I'm not wrong. You are wrong thinking that infinite ends. you can't have a zero at the end of infinite nines.

Infinite is not too short of 1/3 INFINITE DOESNT END. 1/3 equals exactly .3 repeating.

 

[Killer Tree]

Killer Tree, time to go a bit further : what's 0.913749137491374~ equal to ?

x=.91374~
100000x = 91374.91374~
100000x - x = 91374.91374~ - .91374~
99999x = 91374
x = 91374/99999


<_>

 

[Rici]

sigh... even as infinity wouldn't end IT'S STILL TOO SHORT FOR 1/3. You just can't wright 1/3 in decimals, that's why we have 1/3.

Also, explain to me how 10 x 0.999~= 9.999~
Where is the 0 at the end? You can't just replace it with another 9!

Please...

 

[Killer Tree]

sigh... even as infinity wouldn't end IT'S STILL TOO SHORT FOR 1/3. You just can't wright 1/3 in decimals, that's why we have 1/3.

Also, explain to me how 10 x 0.999~= 9.999~
Where is the 0 at the end? You can't just replace it with another 9!

Please...

10 x .9~ move the decimal to the right.....................................................................................
So with your logic 5.5 x 10 does not equal 55 because the zero disapeared?? o.O LOL


Also.... infinite is not too short for 1/3 that doesn't make sense.
Noone writes 1/3 as .3 repeating since it is much simpler and you don't need to explain it to everyone.

Where is your basis on this thought? Your own opinion?

 

[Doraki]

if you write 1/37 in decimals, its digits are repeating too... what can be the length of the repeated part ?

Riciardos, 0.999~ is a limit : sum for n from 1 to infinity of 9 . 10^-n. It's basically what we start writing but we can't ever finish writing it, though we can imagine it going forever.
If you know how to sum geometric series, it's exactly what he has done..

 

[Killer Tree]

<____________<

Someone should give me access to the debate hall cause the only reason this topic exists is because I can't post in the same topic that was created in the debate hall.

 

[rounder_nk]

.999~=x
10x=9.999~
10x - x = 9x
9x=9
1x=1.
.999~ = 1.

Where the **** did you get 9x=9?
10 x 0.999~= 9.99~0 (notice the 0 at the end.. 10 x 0.9= 9.0)
10 x 0.999~ - 0.999~= 9.99~0- 0.999~
this means that
9x= just a little less then 9
x= a little less then 1 = 0.999~

see where I'm going?
so your wrong.

Also, 1/3 can't be written in decimals. Even infinity is just to short for 1/3. So the second one is also wrong.

As far as I know, math has no errors, only some imperfections like you can't devide by 0.

you questioned the wrong part of his equation here.

if you noticed he wrote 10x=9.99~ which just means that 9.99~=9.99~ and not 10.

this theory could still be right however you would need calculus and limits and i'm way too lazy.

 

[Osco316]

As usual, wikipedia delivers.
http://en.wikipedia.org/wiki/Proof_that_0.999..._equals_1

And another website I found
http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html

 

[Lt. Killjoy]

How about this: .9~ is approximately 1.

 

[commonyoshi]

I get it. But how does this benefit anyone in any way? Why did I take a year of algebra to understand this garbage?

 

[rounder_nk]

it depends on your vantage point (as euclid says) if you define infinity as infinite or finite.

 

[bornfidelity.com]

it depends on your vantage point (as euclid says) if you define infinity as infinite or finite.

You understand ^^

The thing with the 10 x 0.99~ = 9.99~ is that you add another decimal to infinity. Adding something to infinity is like... continuing into some other dimension. Completely surreal.
I think Riciardos was trying to say this.

If you follow, logically, you can't add a decimal to infinity, because being able to add something to the value means it wasn't infinite in the first place.
Hence if you're not able to add a decimal to infinity, the outcome of 10 x. 0.99~ would end with ......9999990.
Math does not deal with this correctly by defining infinity as not ending. Because basically, if something is not ending you can never correctly multiply it either. Math has a way to deal with this by notations such as 0.9999~, but as you can see - since according to math 0.999~ = 1 - even math doesn't have a right solution for dealing with infinity.

 

[rounder_nk]

although it does depend on vantage as i said it also is defined in mathematics (seeing as infininty is normally based as infinite) as equaling one. The reason i say this is because when using limits in calculus if the number approaches another one then it equals that number (this isn't a good way to put it but technically in math if you have 1+1/2+1/4+1/8 so on then eventually it reaches one due to limits). Many theoretical mathematitions have most likely toyed with the finite infinity taking that from another vantage point.

 

[Rici]

10 x .9~ move the decimal to the right.....................................................................................
So with your logic 5.5 x 10 does not equal 55 because the zero disapeared?? o.O LOL


Also.... infinite is not too short for 1/3 that doesn't make sense.
Noone writes 1/3 as .3 repeating since it is much simpler and you don't need to explain it to everyone.

Where is your basis on this thought? Your own opinion?

sigh... When did I say that the zero dissappeared with 5.5x10? The answer is 55.0
You just can't do something times infinity because it would end up as infinity!
That's the same as dividing by 0.

Look: 10 x infinity = infinity
But infinity/infinity= 1
So 10=1?

Where is the logic in that? Where did the 10 go? As infinity is not an actual number, you just can't devide or multiply by it.
So the whole logic is just wrong...

As for the 1/3 part. You are using infinity again so it's wrong again.

 

[rounder_nk]

in conclusion .99~=1 end of story.

 

[typh]

oh u so silly.

if .999~ did not equal 1, what's the number in between the two?

ok, my proof sucks.

 

[MDZ]

There's one little flaw in this debate.. And that is..

It is clear you typed out .9, not 1. :D Thus, .9= .9, and 1=1 :D You just manipulated algebra.

 

[rounder_nk]

oh u so silly.

if .999~ did not equal 1, what's the number in between the two?

ok, my proof sucks.

actually that proof is more understandable and straight forward to the average person. Therefore it gets the point across and makes a good (but not in proper mathematical format) proof.

There's one little flaw in this debate.. And that is..

It is clear you typed out .9, not 1. :D Thus, .9= .9, and 1=1 :D You just manipulated algebra.

right but the algebraic proof is wrong which i pointed out a page ago. If you discuss it in limits then if a number infinately approaches another one beyond a tangible end the it is actually that number (this is a proof in calculus).

 

[rounder_nk]

accidental double post.

 

[Rici]

Wait, I forgot to explain where the 0 went.
look we're just gonna do it without the infinity sign:
10 x 0.999 = 9.990
10 x 0.999 - 0.999= 9.990 - 0.999
9x 0.999 = 8.991
1x= 0.999

See? The way you did it is that you had 2 different values for x
Because this is how you did it:
10 x 0.999 = 9.999 < you just replaced this 0 with another 9.
If you want to get it right after that it should be
10 x 0.9999 - 0.999 = 9
But 0.9999 is something else then 0.9990 am I wrong?

That's why you can't use infinity as a number. That's why your logic is flawed.

Please, just try to understand it.

 

[McFox]

I hate math and all people who advocate its use for anything.

 

[Doraki]

Riciardos, can 0.999~ really be a number ?

If it's not a number, then it doesn't exist, end of story.
But if you think it does equal *something*, then, you can't write a number that's between 0.999~ and 1...
And what would 10*0.999~ be ? 0.999~ is 0 followed by an infinity of 9s. It's infinite, it doesn't end anywhere.
now, multiplying by 10 shifts the decimals to the left, you know that. So 10*0.999~ =9.999~: a 9 followed by an infinity of 9s that's also infinite.
Also, what would be 1-0.999~ ? when you try to write down the beginning of 1-0.999~, you end up writing 0.0000.... that should be equal to 0, right ?