Is 1 = 0.9999......

[crazygal]

Because there's no number inbetween 1 and .999....

Besides, math is based on proofs, not beliefs. The quickest proof that I can think of is:
1/3 = .33333333...
2/3 = .66666666...
3/3 = .99999999... = 1

 

[bleeb]

Originally posted by: crazygal
Because there's no number inbetween 1 and .999....

Besides, math is based on proofs, not beliefs. The quickest proof that I can think of is:
1/3 = .33333333...
2/3 = .66666666...
3/3 = .99999999... = 1

1/3 = 0.33333...
2/3 = 0.66666...
3/3 = 1 != 0.99999...

 

[dighn]

it's alive!

 

[dighn]

Originally posted by: Cuda1447
Mathematically this is true, however logically it is not. People claim that math is the only exact science left, but this problem proves its not.



Math is flawed.

how is it not logically true. 0.9r isn't just x many 9's where x is a very large number, x is infinity. i think the problem is people can't really comprehend infinity.

 

[crazygal]

So what you're saying is that fractions with the same denominator but have a numerator that is changing by a constant (in this case 1, ie. 1,2,3), do not grow linearly. right...

Ask someone who is an expert in math, see what they say. I'm sure there's someone with a PhD in math at your local college who wouldn't mind talking to you about it.

 

[spyordie007]

FOR SANITY'S SAKE MODS PLEASE LOCK THIS THREAD!!!

I cant believe this thing has gone on for so long, there never was a valid debate to be made on this topic and this thread just goes to prove how worthless ATOT is and the poor math skills the general public has.

Now please let's just let this thread die.

:|

-Spy

 

[bleeb]

Originally posted by: spyordie007
FOR SANITY'S SAKE MODS PLEASE LOCK THIS THREAD!!!

I cant believe this thing has gone on for so long, there never was a valid debate to be made on this topic and this thread just goes to prove how worthless ATOT is and the poor math skills the general public has.

Now please let's just let this thread die.

:|

-Spy

Why do you want this thread to die? I think its good for the ignorant masses to finally attempt to figure out this difficult problem.

 

[josphII]

Originally posted by: crazygal
Because there's no number inbetween 1 and .999....

Besides, math is based on proofs, not beliefs. The quickest proof that I can think of is:
1/3 = .33333333...
2/3 = .66666666...
3/3 = .99999999... = 1

i dont know whats more annoying people saying .9r != 1 or people thinking this crap above is a proof.

theres only one proof that i know of which is

Proof: 0.9999... = Sum 9/10^n
(n=1 -> Infinity)

= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)

= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)

= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)

= .9/(9/10)

= 1

taken from here

 

[crazygal]

It's not a rock solid "proof" per se but it's better than trying to explain limits and calculus to these ignoramuses.

 

[OokiiNeko]

After doing some research, I think it comes down to this:

In order for us to determine if an equation is true or false, we must be able to define the terms on either side.

In the case of .999...=1, we can define 1, but we cannot define .999....

This was alluded to in my much earlier posts about the set theory paradox when dealing with infinity.

Does .999...=1?

We don't know.

 

[vtqanh]

Originally posted by: crazygal
Because there's no number inbetween 1 and .999....

Besides, math is based on proofs, not beliefs. The quickest proof that I can think of is:
1/3 = .33333333...
2/3 = .66666666...
3/3 = .99999999... = 1

that is such a piece of crap

 

[crazygal]

OokiiNeko = big cat!

 

[crazygal]

Fine vtqanh, if that's crap as you say, then explain to me why this doesn't work:

Proof: 0.9999... = Sum 9/10^n
(n=1 -> Infinity)

= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)

= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)

= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)

= .9/(9/10)

= 1




That's what I thought

 

[OokiiNeko]

OokiiNeko = big cat!

Ohayo gozaimasu

 

[crazygal]

?!?!?!
It's not morning
Konichiwa!

 

[OokiiNeko]

Ima wa ju-ji nijuni fun in Nihon.

Does .999... = 1?

Zen zen wakaranai!

 

[crazygal]

Ah, soo desu ne!

Ima wa roku-ji niju roku fun de Amerika!

Hajimemashite!

Oh and I believe we CAN define .9999.... just as we can define .33333.... or .6666.... or anything else for that matter.

 

[vtqanh]

Originally posted by: crazygal
Fine vtqanh, if that's crap as you say, then explain to me why this doesn't work:

Proof: 0.9999... = Sum 9/10^n
(n=1 -> Infinity)

= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)

= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)

= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)

= .9/(9/10)

= 1




That's what I thought

Where/When did i say that this didn't work?

This is probably the most elegant proof for this problem. I still prefer the simple proof (10x-x) though.

But the 1/3 = 0.3333...(correct), 2/3=0.66666...(absolutely), 3/3=.99999....(huh?) is not even close to a proof

 

[crazygal]

I admit I used "proof" loosely but alas it is still true.

 

[dighn]

Originally posted by: vtqanh

Originally posted by: crazygal
Fine vtqanh, if that's crap as you say, then explain to me why this doesn't work:

Proof: 0.9999... = Sum 9/10^n
(n=1 -> Infinity)

= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)

= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)

= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)

= .9/(9/10)

= 1




That's what I thought

Where/When did i say that this didn't work?

This is probably the most elegant proof for this problem. I still prefer the simple proof (10x-x) though.

But the 1/3 = 0.3333...(correct), 2/3=0.66666...(absolutely), 3/3=.99999....(huh?) is not even close to a proof

whwat's wrong with 3/3 = 0.99999 ?
1/3 = 0.33333... = (3/10 + 3/100 + 3/1000 ...) if you multiply by 3 that's (9/10 + 9/100 + 9/1000...) which is exactly the defintion of 0.9r

 

[OokiiNeko]

Hajimemashite!

Yuroshiku. (or is it Yoroshiku?)

Actually, can you say with definitive and ultimate authority that .333..... is greater or less than .444.... ?

Or that infinity is greater or less than infinity + 1 ?

We can manipulate the representations of the concept of infinity all we want, we still don't know.

Honto!

 

[crazygal]

Yoroshiku actually

well .333... is exactly equal to 3/9 and .444... is exactly equal to 4/9 (by the simple rules of math) so we can say with authority which is bigger.

However, you're right that we can manipulate things quite easily. But there's still a problem with your reasoning:
there's a proof stating that .999.... = 1 but there's not a proof that disagrees.

Unless you can disprove this:
Proof: 0.9999... = Sum 9/10^n
(n=1 -> Infinity)

= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)

= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)

= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)

= .9/(9/10)

= 1

then we don't need to look further.

Jane!

 

[OokiiNeko]

well .333... is exactly equal to 3/9 and .444... is exactly equal to 4/9

We don't really know that.

= lim .9(1-10^-(m+1))/(9/10)

= .9/(9/10)

Not being a math wiz, explain what happened between these two steps, onegai shimasu.

 

[dighn]

it was taking the limit as m approaches infinity. so 10^-(m+1) diminishes to 0

 

[josphII]

good god..... saying 1/3 = .333..., 2/3=.666..., 3/3=.333... is NOT a proof, nor is the 10x-x "method"

in order to proove that .999... = 1 you can not start off with a number that is a subset of .999... In the case of the [1/3 = .333..., 2/3=.666..., 3/3=.333...] you are starting off with .999... / 3, which still begs the question, where did you get .999...