Is 1 = 0.9999......

[spyordie007]

Originally posted by: ElFenix
you know, deep down in your soul, that pound of bricks is just a tiny bit heavier than that pound of feathers

This must be Madrat math....

"even though we have proved that they weigh the same I just dont think they are the same and therefore they are not!"

Thanks for the proofs Ross, I just wish that some people would get the idea in their head that ".999*" is not an infinite number, it just has an infinite length, and on the number line it occupies the exact same point as "1".

-Spy

EDIT: fixed my punctuation

 

[Skyclad1uhm1]

Originally posted by: element®

Originally posted by: Skyclad1uhm1

Originally posted by: RossGr

Originally posted by: Skyclad1uhm1

Originally posted by: RossGr
This topic is not about rounding.

what is the point of .999... = 1.0
or
.999... = 1.00.....
The extra zeros mean nothing.

I was a pilot for years.


They told me to pick it up over here and pilot over there.


I am very glad you are studying avition, should we be impressed? What is of interest in this thread is what math you are studying.

What math nobelprize did you win, to be smarter than college professors quoted here?

College professor quoted where?

Check my post on Hackenstrings.

Edit: I agree with 0.999... = 1 in most circumstances, but not with just bringing infinity into a calculation about Real numbers to prove something. Infinity is not a number you can work with the same way you do with ordinary numbers, 10 * 0.999... - 0.999... does not give 9 just like that. That is like saying infinity - 1,000,000 = infinity, infinity - infinity = 0, give me $1,000,000 and you lose nothing!

You are mistaken. If I have an infinite number of dollars, and I give you $1,000,000 I DO lose nothing! The fallacy here is that I cannot ever have an infinite number of dollars, but the math still holds. Infinity can be used as a number of sorts. Infinity - $1,000,000 does equal infinity. And infinity-infinity does=0.

and 0.9999... does =1 !!!

I say again, you naysayers need to find a number between 1 and 0.999...
Stop trying to evade the question. You cannot find a number between 1 and 0.999... because it would be 0.0000 (infinite zeros go here) 0000001 but you can never write that last 1 !!!! you have to keep writing zeroes! so 1-0.99999...=0.0000000

Therefore 1=0.9999...

If you use infinity for 'normal calculations' you get a mess:

infinity - infinity = 0
2*infinity = infinity
so infinity - (2*)infinity = -infinity
(2*)infinity - infinity = infinity

infinity - infinity can be any number between + and - infinity.

 

[spyordie007]

Originally posted by: Skyclad1uhm1

Originally posted by: element®

Originally posted by: Skyclad1uhm1

Originally posted by: RossGr

Originally posted by: Skyclad1uhm1

Originally posted by: RossGr
This topic is not about rounding.

what is the point of .999... = 1.0
or
.999... = 1.00.....
The extra zeros mean nothing.

I was a pilot for years.


They told me to pick it up over here and pilot over there.


I am very glad you are studying avition, should we be impressed? What is of interest in this thread is what math you are studying.

What math nobelprize did you win, to be smarter than college professors quoted here?

College professor quoted where?

Check my post on Hackenstrings.

Edit: I agree with 0.999... = 1 in most circumstances, but not with just bringing infinity into a calculation about Real numbers to prove something. Infinity is not a number you can work with the same way you do with ordinary numbers, 10 * 0.999... - 0.999... does not give 9 just like that. That is like saying infinity - 1,000,000 = infinity, infinity - infinity = 0, give me $1,000,000 and you lose nothing!

You are mistaken. If I have an infinite number of dollars, and I give you $1,000,000 I DO lose nothing! The fallacy here is that I cannot ever have an infinite number of dollars, but the math still holds. Infinity can be used as a number of sorts. Infinity - $1,000,000 does equal infinity. And infinity-infinity does=0.

and 0.9999... does =1 !!!

I say again, you naysayers need to find a number between 1 and 0.999...
Stop trying to evade the question. You cannot find a number between 1 and 0.999... because it would be 0.0000 (infinite zeros go here) 0000001 but you can never write that last 1 !!!! you have to keep writing zeroes! so 1-0.99999...=0.0000000

Therefore 1=0.9999...

If you use infinity for 'normal calculations' you get a mess:

infinity - infinity = 0
2*infinity = infinity
so infinity - (2*)infinity = -infinity
(2*)infinity - infinity = infinity

infinity - infinity can be any number between + and - infinity.

and the whole point was that you cant work with infinity the same way you do with ordinary numbers, not that it matters because .999* is not infinity it is mearly a repeating non-terminating decimal and like I said before occupies a single point on the number line (1).

-Spy

 

[james88]

infinity - infinity can be any number between + and - infinity.

there is no negative infinity right?

 

[silverpig]

Originally posted by: james88

infinity - infinity can be any number between + and - infinity.

there is no negative infinity right?

Sure there is...

-1, -2, -3, ... -100 000 000, ... -infinity

 

[bleeb]

0.9999.... != 1

 

[MadRat]

Originally posted by: spyordie007

Originally posted by: ElFenix
you know, deep down in your soul, that pound of bricks is just a tiny bit heavier than that pound of feathers

This must be Madrat math....

I don't know what you're trying to say here. It does remind me of the teaser comparing the ounce of gold to the ounce of feathers.

 

[RossGr]

Infinity is "tacked on to the set of real numbers in the folloing manner.
first let me define I = infinity, just so I dont Have to type infinity so many times.

I > x for all x in R
-I < x for all x in R

Let x be any element of R
x + I = I
x * I = I x>0 -I if x<0

x - I = - I


Well I am attempting to post this from memory, not working to well when get back to my referernce I will update this post.

The point is in the world of Real Analysis the meaning of, and operations on I are carefully definined

The formal name for the three periods which appear at the end of .99... is the ellipsis. If propererly used it implies a continuation of the given pattern to infinity when it appears at the END of a number. If it appears in the middle it inticates the ommision of a FINITE number of digits so .000...001 is not an infinite string of zeros followed by a 1. Such a notion is selfcondictory since the term infinite implies a never ending string, the placement of a 1 MUST be in a fixed decimal loction so as soon as it is set in place you have defined a finite location. If the ellipsis is used correctly there is no inconsistancy.

 

[josphII]

its obvious from reading many posts in this thread that basically everybody that thinks that 1 != 0.999... doesnt understand the concept of infinity

two common errors in this thread:

the difference between 1 and 0.999... is 0.000...1, thus 1 != 0.999... , this is incorect because there is no number 0.000...1 because you can not have an infinite number of zeros and then another number after. infinity, by definition, has no end so how can you have a digit 1 after an infinte number of zeros? you cant! 1 - 0.999... == 1 -1 = 0

infinity - infinity does NOT equal 0. any attempt to rationalize your incorrect theory that 1 != 0.999... by somehow applying basic mathmatical functions (+, - , * , or /) on infinity is greatly flawed.

 

[bleeb]

its obvious that 0.9999.... != 1

 

[TuxDave]

Originally posted by: bleeb
its obvious that 0.9999.... != 1

dieeee.... you sound like one of my evil professors who always used the word 'obvious'. But I dunno what you're talking about, it's quite intuitive that 0.999... = 1.

 

[bleeb]

hahah i'm just messing with everyone

 

[Skyclad1uhm1]

Btw, for x < 1, what is the largest x possible?

 

[TuxDave]

Originally posted by: Skyclad1uhm1
Btw, for x < 1, what is the largest x possible?

None exists? (according to a philosophy class). They also proposed a question, imagine two line, one rotating and the other still. At one point, the two lines will be parallel. At some time in the future, they will be crossed, where's the first point of contact? Does it exist?

And so... I have no idea why I just mentioned that...

 

[heliomphalodon]

Oh, for cryin' out loud. How can you have a "poll" on this?
There can be no debate here, only protestations and expressions of ignorance.
It would make just as much (actually, as little) sense to have a poll on whether "1+1=2" is a true statement.

The fact is, the "symbol" 0.999999... is defined in such a way that it is equal to 1.
In the absence of a sharp definition, one cannot even ask whether 0.999999... equals 1 or not.

What's really disappointing is that "no" is leading in the poll.

 

[element]

Originally posted by: Skyclad1uhm1
Btw, for x < 1, what is the largest x possible?

I'll answer your question if you answer mine first, since I asked mine first. Since you contend that 0.9999... is not equal to 1, then what number lies between 0.9999... and 1?

 

[BennyD]

Originally posted by: element®
what number lies between 0.9999... and 1?

0.9999... and a half?

 

[element]

Originally posted by: TuxDave

Originally posted by: Skyclad1uhm1
Btw, for x < 1, what is the largest x possible?

None exists? (according to a philosophy class). They also proposed a question, imagine two line, one rotating and the other still. At one point, the two lines will be parallel. At some time in the future, they will be crossed, where's the first point of contact? Does it exist?

And so... I have no idea why I just mentioned that...

This probably deserves its own thread as it is going off on a tangent...ahhha no pun intended but a punny made nonetheless!

But first of all define a line. Do you mean an inifinitely long ray? This does not physically exist of course. If you mean a finite line of finite length and width then the point at which they touch depends on the instrument you use to determine that point. It depends on our resolution of accuracy in determining when they touch. This is ever changing as technology improves and resolutions increase to see as smaller levels. (Atomic, subatomic...etc...)

 

[element]

Originally posted by: BennyD

Originally posted by: element®
what number lies between 0.9999... and 1?

0.9999... and a half?

A half being 0.5, would make 0.999... and a half = 1 1/2
No soory, sooory 1 1/2 is greater than 1.

NEXT!

 

[silverpig]

Originally posted by: element®

Originally posted by: BennyD

Originally posted by: element®
what number lies between 0.9999... and 1?

0.9999... and a half?

A half being 0.5, would make 0.999... and a half = 1 1/2
No soory, sooory 1 1/2 is greater than 1.

NEXT!

No soup for you! Come back 1 year!

 

[heliomphalodon]

Originally posted by: Skyclad1uhm1
Btw, for x < 1, what is the largest x possible?

What you're asking is: "Does the open interval (0, 1) contain a largest element?"
The answer is: "No, it doesn't."

One might as well ask: "What is the smallest positive real number?"

 

[silverpig]

The answer, of course, is: There isn't one.

No matter what number you give me, I can always divide it by 2 (or a million for that matter) to get a number closer to 0.

 

[TuxDave]

Originally posted by: element®

Originally posted by: TuxDave

Originally posted by: Skyclad1uhm1
Btw, for x < 1, what is the largest x possible?

None exists? (according to a philosophy class). They also proposed a question, imagine two line, one rotating and the other still. At one point, the two lines will be parallel. At some time in the future, they will be crossed, where's the first point of contact? Does it exist?

And so... I have no idea why I just mentioned that...

This probably deserves its own thread as it is going off on a tangent...ahhha no pun intended but a punny made nonetheless!

But first of all define a line. Do you mean an inifinitely long ray? This does not physically exist of course. If you mean a finite line of finite length and width then the point at which they touch depends on the instrument you use to determine that point. It depends on our resolution of accuracy in determining when they touch. This is ever changing as technology improves and resolutions increase to see as smaller levels. (Atomic, subatomic...etc...)

I meant an infinitely long ray... it's more of a thought experiment but it cannot be realized in this physical world.

 

[AznMaverick]

Originally posted by: element®

Originally posted by: BennyD

Originally posted by: element®
what number lies between 0.9999... and 1?

0.9999... and a half?

A half being 0.5, would make 0.999... and a half = 1 1/2
No soory, sooory 1 1/2 is greater than 1.

NEXT!

0.9999..../2.

 

[thraashman]

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

Ok, for this problem to work, 0.999999..... assumes and infinite number of 9's. The problem occurs here
9.9999... - 0.9999... , both assume an infinite number of 9's, the problem is that you cannot subtract and infinite from and infinite.

The reason a problem like this works in Calculus, is that in Calculus, you work with limits. And limits mean a number that is all but achievable. in calculus, 0.99999999...... is the limit as n approaches infinity of 9/(10)^n, 1 is the answer, because 1 is what that number can get infinitely close to, but never quite achieve, therefore in calculus, you assume equivalence because there is no distinguishable difference in value. The best example of this is when someone said 1 - 0.999999999......, and that with an infinite number of 9's, the 1 that should exist after all the 0's, never really exists, and the answer is 0.000000000.... there is a difference, but you can never prove the difference because there are and infinite number of 0's.

So, in other words, 1 != 0.999999.... , but the difference is indistinguishable and for all logical purposes, equivalence is assumed.