.9~=1

[bornfidelity.com]

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.

The thing there is, do you consider 0.999~ to be absolute or subject to change. When you multiply 0.999~ by 10, you add another 9 at the end, but if you then divide the outcome by 10 again, you've added a decimal to infinity.
Being able to add something to a value means it wasn't infinite in the first place, hence infinity =/= infinity.
And that's obviously not right either.
-> Math can't deal with infinity.

 

[Doraki]

LOL bf, why would 0.999~ be subject to change ? 0.999~= 0.999~ and that's it, right ?
infinity + 1 = infinity. problem solved ? And, btw, tell me exactly which decimal we add by doint 0.999~ x 10 / 10.
Remember, infinity doesn't end.

 

[Helios]

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

You mean like, computer scientists, for example? ****ing binary....

 

[rounder_nk]

once again the only conventional way to prove this is with limits. All limits say is that if a number approaches another one then it takes on the identitiy of that number. Another way to prove this is that .999~ can be defined as the sum of an infinite geometric series:

.999~=.9+.9(1/10)+.9(1/10)^2 so on

since the common ratio 1/10 is less than one (in absolute value) it follows from the convergence theorem that the series converges and its sum is

.9/(1-(1/10))=1

personally though i'm a fan of what number would lie between them? as typh put it.

 

[Wenbobular]

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

But without math we probably wouldn't have Smash...or any other video game for that matter. With all the physics stuff and such...
And binary is easy! Well. I can count to 15 fast enough.
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
That's what I learned in elementary computer science...I think they called it fundamentals...

 

[bornfidelity.com]

LOL bf, why would 0.999~ be subject to change ? 0.999~= 0.999~ and that's it, right ?
infinity + 1 = infinity. problem solved ? And, btw, tell me exactly which decimal we add by doint 0.999~ x 10 / 10.
Remember, infinity doesn't end.

Yes, infinity doesn't end, but that's where the problem in math lies. infinity + 1 = infinity? NO.
Mathematically, A + B =/= A. that's not possible. A + B = A + B. According to mathematical rules.

the infinite amount of decimals = A
A + 1 = A + 1.
(0.999~ (A decimals) x10 = 9.999~, added one decimal (A + 1 Decimals)).
(9.999~ (A + 1 decimals)/10 = 0.999~ (moved the dot the the right so amount of decimals doesn't change, hence still (A + 1 decimals))

^ According to tis 0.999~ (A) = 0.999~ (A+1)
A = A+1 is not possible.
Hence math does not deal with infinity adequatly.

RounderNK; the value inbetween .999~ and 1 is only describable as
0.999~ < X < 1.

 

[rounder_nk]

right but .999~ is an infinite number (unless you're defining infinity as some finite number which is for the most part incorrect seeing as infinity is a concept not a number). The only way to deal with a number of this calibre is to take into consideration limits and the limit says that if a number approaches something then it takes on that value. You were treating infinity as a real number which in actual mathematics is false. Unless you can actually obtain that x that you described then that theory isn't possible. Since infinity is an undefined variable then it is impossible to add anything to it. In algebraic problems when you have anything/0 then it's undefined (or infinite) you can't add anything to an undefined number.

Another thing is take into consideration this- 1/0-infinity therefore 1/0+1 is actually 1/0+0/0 (which is the only way to make the denominators the same seeing as you can' multiply 0 by anything to get another variable) therefore 1/0+1=1/0. (since there is no possible way to rationalize the denominators then it's impossible to add the two terms). Another thing is that say you divide infinity by a number like 2. 1/0/2 then 0/2 which is still 0 and finally this equals 1/0 still.

 

[bornfidelity.com]

right but .999~ is an infinite number (unless you're defining infinity as some finite number which is for the most part incorrect seeing as infinity is a concept not a number). The only way to deal with a number of this calibre is to take into consideration limits and the limit says that if a number approaches something then it takes on that value. You were treating infinity as a real number which in actual mathematics is false. Unless you can actually obtain that x that you described then that theory isn't possible. Since infinity is an undefined variable then it is impossible to add anything to it.

0.999~ has to be defined as ending for it to work in math, but endless for it to react to reality. Like you said, infinity is a concept rather than a number (a value), and math can only deal correctly with values, not with concepts that can't be given a value. the 0.999~ = 1 theory prooves that; it's mathematically correct and incorrect at the same time thus logically incorrect.

 

[Doraki]

Bf.com.......

The thing is to decide what's a real number.
Is 1/0 a real number ? can you do operations with it ?

+ and * only works between numbers. infinity + something makes NO SENSE, when you ONLY know about adding NUMBERS.

Are things like 0.999~ real numbers ? After all, you can't write it completely, right ? So why would it exist ?
If so, you should be able to do (10*0.999~)/10 and find the exact SAME number. And not discover that it has one less decimal than infinity o_O.
because 10*(a number)/10 = that number. Always. You can't deny that.

How do you understand 0.999~ ? How do you perform operations on it ?
After all, you were told that 1/3 DOES equal 0.333~ so why not 0.999~ ?

the set {1,2,3,4,5,.......} is infinite. right ?
now, add 0 to it. you get {0,1,2,3,4,5,....}. it's also infinite. And the function x -> x-1 on N* is a bijection between the 2 sets. If I decided to rename 1 into 0, 2 into 1, 3 into 2 etc..... it would be the same infinite set.
They're the "same" infinites even though you added 1 element to the first set.

I don't want to go into ordinals theory, but the Zermelo-Fraenkel Set Theory can describe infinite sets, order them and make additions and multiplications between them. So don't say that math don't handle infinites...

A classic way to understand 0.999~ is as the limit of the sequence 0.9, 0.99, 0.999, 0.9999 ... etc..
Those numbers gets closer and closer to 1, and in standard real numbers theory, that proves that the limit equals 1.
In any case, 0.999~ is greater than any 0.999...9 with a finite amount of 9s, ok ?
So 1 - 0.999~ is less than 0.000....001, with any number of 0s before the 1. So the difference is less than 10^-n for every n.
Saying that 0.999~ doesn't equal 1, is the same as saying that there's a number epsilon that is > 0 and < any positive standard real number.

 

[rounder_nk]

^^correct

any calculus professor and textbook will tell you that this is the case.

 

[bornfidelity.com]

Bf.com.......

The thing is to decide what's a real number.

+ and * only works between numbers. infinity + something makes NO SENSE, when you ONLY know about adding NUMBERS.

That's why math & infinity don't comply realistically; because infinity isn't a value (number).
In order to work with infinity, mathemetically you have to make infinity ending somewhere, and then the stuff I said before does apply.
Obviously what I said is bullocks when applying to realistic infinity, the infinity you've been using.

The difference between 0.999~ and 1 doesn't exist when using this realistic infinity, but using and ending infinity - like, mathematically - the difference is the same as the difference between the smallest possible value and nothing.

...all I was saying, infinity is too abstract for maths to deal with accordingly. That's all

 

[SuperBowser]

isn't this like the first thing you learn before differentiation...?

our class was having none of it and we argued about it over and over for a good 4 months >: (

 

[bornfidelity.com]

isnt differentation the first thing you learn at all?

 

[Doraki]

lol @ bf saying "ending infinity". Infinity is infinite, you know ? Infinite is not abstract at all, we know very well what it's like.
anyway I'm done talking to you you won't change your mind apparently.

 

[SuperBowser]

*stabs*

you know what i mean

or at least that's how we learned differentiation.

 

[Killer Tree]

The thing there is, do you consider 0.999~ to be absolute or subject to change. When you multiply 0.999~ by 10, you add another 9 at the end, but if you then divide the outcome by 10 again, you've added a decimal to infinity.
Being able to add something to a value means it wasn't infinite in the first place, hence infinity =/= infinity.
And that's obviously not right either.
-> Math can't deal with infinity.

Your logic is wrong, you can add to infinite. 1 plus infinite is still infinite and i still added. You are aloud to move the decimal over.

 

[Killer Tree]

Yes, infinity doesn't end, but that's where the problem in math lies. infinity + 1 = infinity? NO.
Mathematically, A + B =/= A. that's not possible. A + B = A + B. According to mathematical rules.


0.999~ < X < 1.

Ok there is not number in between them.

Also.... a=1 b=0

a+b=a

Now are you going to try to convince me that math doesn't work with zeros either?

0.999~ has to be defined as ending for it to work in math, but endless for it to react to reality. Like you said, infinity is a concept rather than a number (a value), and math can only deal correctly with values, not with concepts that can't be given a value. the 0.999~ = 1 theory prooves that; it's mathematically correct and incorrect at the same time thus logically incorrect.

'

WHERE DO YOU GET THIS INFORMATION? Calculus and higher math deal with infinite all the time,

That's why math & infinity don't comply realistically; because infinity isn't a value (number).
In order to work with infinity, mathemetically you have to make infinity ending somewhere, and then the stuff I said before does apply.
Obviously what I said is bullocks when applying to realistic infinity, the infinity you've been using.

The difference between 0.999~ and 1 doesn't exist when using this realistic infinity, but using and ending infinity - like, mathematically - the difference is the same as the difference between the smallest possible value and nothing.

...all I was saying, infinity is too abstract for maths to deal with accordingly. That's all

Math isn't realistic in the first place. The square root of negative 1 is i. Try figuring that out realistcaly. You can't do it realistcly but you can graph it mathematicly,

 

[Killer Tree]

Sorry double post

 

[bornfidelity.com]

Ok there is not number in between them.

Also.... a=1 b=0

a+b=a

Now are you going to try to convince me that math doesn't work with zeros either?

,

lol you got me there

sorry sometimes I find joy in talking crap and seeing if people buy it or not

 

[digitalmaster287]

Zero and infinity both follow special rules that no other "number" follows. You cannot divide by zero because it simply isnt logical and in the same way, you cannot do anything with infinity. All 0.99999~ is jus basically 1 - (1/infinity). You also cant say that 0.9999~=1 because 0.9999~ =3(1/3) because 1/3 which becomes 0.33333~ which never actually reach one third exactly, but instead will only get closer and closer. The same way, 0.9999~ will never reach 1 because it will only get closer and closer. If there were truly an infinite about of 3s at the end of 1/3 , then it simply would become 1 after being multiplied by 3 and would never become 0.999~.

 

[Rici]

Yep, that 1/3 part that you posted, you say that it's proof that 0.9~=1
I say it's proof that 1/3 can't be written as a decimal number.

As for the A+B part
A+B = A+B

So 1 + 0 = STILL 1 + 0
What you say is
Infinity + 1 ( A+B) = Infinity(A)
But where did the 1(B) go?

 

[Doraki]

The same way, 0.9999~ will never reach 1 because it will only get closer and closer. If there were truly an infinite amount of 3s at the end of 1/3 , then it simply would become 1 after being multiplied by 3 and would never become 0.999~.

Hmm.. it's pretty obvious to me that 3 * 0.3333~ = 0.9999~ and 0.9999~ /3 = 0.3333~.

and, if 0.9999~ is a real number, it doesn't move. It has a fixed value and doesn't get closer and closer to anything....
howver, the sequence 0.9, 0.99, 0.999, ... gets closer and closer to 1, just as 0.3, 0.33, 0.333, ... gets closer and closer to 1/3.

 

[rounder_nk]

for the last time if a number infinitely approaches another number then it takes on the value of that number according to limits. ITS A MATHEMATICAL PROOF WHICH NO MATTER HOW MUCH ARGUING WILL STAY THE SAME. Theoretical mathematicians might change it if the debate over infinity changes course but for now that is a pretty solid proof in calculus.

 

[Killer Tree]

Zero and infinity both follow special rules that no other "number" follows. You cannot divide by zero because it simply isnt logical and in the same way, you cannot do anything with infinity. All 0.99999~ is jus basically 1 - (1/infinity). You also cant say that 0.9999~=1 because 0.9999~ =3(1/3) because 1/3 which becomes 0.33333~ which never actually reach one third exactly, but instead will only get closer and closer. The same way, 0.9999~ will never reach 1 because it will only get closer and closer. If there were truly an infinite about of 3s at the end of 1/3 , then it simply would become 1 after being multiplied by 3 and would never become 0.999~.

Auctually 1/infinite = zero

 

[Rici]

So you are saying that zero x infinity = 1?

 

[Uncle Meat]

He's either dreadfully stupid or terrible misinformed.

EDIT: Oops, nevermind.

 

[digitalmaster287]

If 0.999~ does equal 1, then that means that 1- (1/infinity) =1 which would say that 1/infinity =0. So then 0*infinity=1?

 

[rounder_nk]

here

you all are terribly butchering an already proven concept (that being .99~=1). So for the lasdt time this is true.

another thing is that 1/0 doesn't equal infinity. It's an undefined concept seeing as nothing can be divided by zero.

1/0 is said to be undefined because division is defined in terms of
multiplication. a/b = x is defined to mean that b*x = a. There is
no x such that 0*x = 1, since 0*x = 0 for all x. Thus 1/0 does not
exist, or is not defined, or is undefined.

 

[Rici]

I still think that that whole concept is wrong. Just because a number is getting closer to another number doesn't make it the same number. It just makes it getting closer and closer.

And haven't I disproven this yet?
x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

10x isn't 9.9999~ as you are just removing a 0. For that alone this whole logic is flawed.
If you want to get it right you have to write 9.999~0 so 9.999~0 - 0.999~= 8.999~1
Then 1x= 0.999~ again.
THEN IT'S RIGHT.
Because that's what the solution is supposed to be.

Saying that 0.999~=1 is the same as saying that 2=1 because why wouldn't we just remove/add numbers?(sarcasm)

Dr. Math can kiss my ***.

 

[rounder_nk]

I still think that that whole concept is wrong. Just because a number is getting closer to another number doesn't make it the same number. It just makes it getting closer and closer.

And haven't I disproven this yet?
x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

10x isn't 9.9999~ as you are just removing a 0. For that alone this whole logic is flawed.
If you want to get it right you have to write 9.999~0 so 9.999~0 - 0.999~= 8.999~1
Then 1x= 0.999~ again.
THEN IT'S RIGHT.
Because that's what the solution is supposed to be.

Saying that 0.999~=1 is the same as saying that 2=1 because why wouldn't we just remove/add numbers?(sarcasm)

Dr. Math can kiss my ***.

to each their own. If you want to go through life with a flawed concept be my guest. Stubborness won't get you many places.

another thing is that i refuted that algebraic equation many times. The only waay to explain it is to know that that's what limits designate as 1. It's a simple proof that for the most part holds no significance to anything. So therefore get over it.

 

[bornfidelity.com]

to each their own. If you want to go through life with a flawed concept be my guest. Stubborness won't get you many places.

another thing is that i refuted that algebraic equation many times. The only waay to explain it is to know that that's what limits designate as 1. It's a simple proof that for the most part holds no significance to anything. So therefore get over it.

Actually, the thing Riciardos is saying is logically right, just not mathematically. Mathematically this is correct because (obviously) math is flawed when working with infinitism.

Hey I repeated myself. Cool. ^^

But well basically, everyone is right, because mathematically this is right. Riciardios is not approaching this mathematically but logically.

 

[Doraki]

Wow, Riciardos, you NEED to explain me your concept of MOVING NUMBERS !!! I love that !!!!!!!!!!

10x isn't 9.9999~ as you are just removing a 0. For that alone this whole logic is flawed.
If you want to get it right you have to write 9.999~0 so 9.999~0 - 0.999~= 8.999~1
Then 1x= 0.999~ again.
THEN IT'S RIGHT.
Because that's what the solution is supposed to be.

You seem to think that there's a finite number of decimals when you say 9.999~. But no, it was said that there was an INFINITE number of decimals, thus, there is NO END of it, and thus, you can't write another decimals after them.

edit, bf, don't EVER use the word mathematically again.
mathematically true means true.
mathematically false means false.
oh and don't EVER say that maths are (obv.) (!!!) wrong about something. ever.

 

[Rici]

Ofcourse you can put something after an infinite number of decimals.
Look:
0.91
0.991
0.9991
0.99991
ect. ect.
Why can you (somehow) write an infinite of numbers(which just can't... infinity eh?) at the end of a number and can't write it between decimals??
The list with nines just keeps growing, as the 1 stays at the end.
This way your not replacing the 1 with another 9.

The 9's don't end.. it's just that it's somehow followed by a 1.

 

[Doraki]

Then you're saying that 0.999~ = 0.(infinite number of 9s) = 0.(infinite number of 9s)9 (as in putting a nine after the infinite number of nines),
and 10 x 0.999~ = 9.(infinite number of 9s)0 ?

Do you agree that when you put a 0 at the end of a number's decimals, that number doesn't change ?
Then 0.999~ is also equal to 0.(infinite number of 9s)0.
But then 0.999~ - 0.999~ = (0.(infinite number of 9s)9) - (0.(infinite number of 9s)0)
= 0.(infinite number of 0s)9
though it should be exactly 0 ?

 

[Killer Tree]

Actually, the thing Riciardos is saying is logically right, just not mathematically. Mathematically this is correct because (obviously) math is flawed when working with infinitism.

Hey I repeated myself. Cool. ^^

But well basically, everyone is right, because mathematically this is right. Riciardios is not approaching this mathematically but logically.

How is math flawed? This is also logically right because Riciardios is thinking infinite can end.

Ofcourse you can put something after an infinite number of decimals.
Look:
0.91
0.991
0.9991
0.99991
ect. ect.
Why can you (somehow) write an infinite of numbers(which just can't... infinity eh?) at the end of a number and can't write it between decimals??
The list with nines just keeps growing, as the 1 stays at the end.
This way your not replacing the 1 with another 9.

The 9's don't end.. it's just that it's somehow followed by a 1.

No thats wrong. Infinite would have to end for that to be correct.

 

[Killer Tree]

So you are saying that zero x infinity = 1?

http://en.wikipedia.org/wiki/Infinite

Zero x infinite = undefined

 

[Killer Tree]

∞ lets use that symbol for now on.

 

[Office_Shredder]

riciardos, it may interest you to know that I actually attempted to comprehensively develop a "super-infinite" decimal place algebra. I'm sorry to say that it is not a closed group under multiplication (what's .0~1*10?), and thus can't really be taken into consideration

 

[digitalmaster287]

if 0.999~(10)=9.999~ , then what would happen if you were to multiply 0.9999~ by infinity? there would then be an infinite amount of nines. But if 0.999~ and 1 are really equal, then wouldnt u also get an infinite amount of nines when you multiply 1 by infinity? no, you get 100000~ which is one greater than 9999~ .

 

[Killer Tree]

if 0.999~(10)=9.999~ , then what would happen if you were to multiply 0.9999~ by infinity? there would then be an infinite amount of nines. But if 0.999~ and 1 are really equal, then wouldnt u also get an infinite amount of nines when you multiply 1 by infinity? no, you get 100000~ which is one greater than 9999~ .

ummmmmmmm any positive number times infinite = infinite


WTF @ your logic

And even if your logic DID make sense, 99999999~ = 100000000~ since they are both infinite