Poll: Does 0.999.. equal 1 ?

[Rough Sausage]

The gap is infinitely small, but there is a gap.

Plus anyone who says they are the same is clearly a pretentious retard desperately trying to look clever to cover the fact that he has below average IQ and has a small penis.

So yeah >.>

Find the flaw in this logic

1/9 = 0.111111111111111...
0.111111111111111... * 9 = 0.99999999999999999...
Therefore 9/9 = 1 and 0.9999999999999...

Numbers cannot be synonyms. That is the flaw in this logic.

Statement: Numbers cannot be synonyms.
Counter example: 2/2 = 1/1 = 1. A synonym is the use of a different word to convey the same meaning; here I have used 2 different expressions for the number 1.

But those aren't single numbers are they? That's like if I said there was no synonym for silver (I don't care if there is) and you countered with "Silver!"

Either way, my argument shows there are at least 2 ways to write any one number, do you dispute this?

2/2 is a sum; it literally means 2 divided by 2. It is more than one number.

What I am saying is that there is no way of writing the same (single) number in two different ways.

2/2 is an expression, not a sum. Summing is specifically the act of adding numbers together. Expressions are similar to equations, but they are missing one key element of equations: They do not have an equals sign in them. 2/2 is an expression, 2/2 = 1/1 is an equation, and neither are sums.

 

[akfg666]

1x=0.9999999999999
10x=9.999999999999
10x-1x= (9.9999999999-0.99999999999)=9
9x=9
9/9=1

^.^

 

[maninahat]

yes, if you are an Engineer.
no, if you are a Mathematician

It's more the other way around actually. The engineer is the on likely doing calculations by saying "whatever, it's there but just infinitely small" while the mathematicians would mess around with limits and such.

But I guess this is a troll thread. Not only is a large amount voting no, but a majority is. WoW!

There's no rounding going on, there's no approximation, it's no "flaw" in our mathematics involved, a !quirk" in the decimal system, but no flaw.

But whatever, if multiple proofs are not enough (it should be, ONE correct proof should be enough actually) and you think that somehow all the mathematicians in the world got it wrong and YOU are the only one to see the truth, you come up with a proof for your side.

Here, I'll help with the start because there's one really simple way to prove that they are in fact not equal. Here it is:

Find a number x such that:

0.999... < x < 1

If there is a number that fits between them, xlearly they are not equal. And I'll say it right now that no, "zero point zero with an infinite amount of zeroes and then a one" does not work, because if there's an infinit amount of something there's no "and then".

hmm, not sure where you are getting with this post. Ok, 0.9999.... is not 1 in reality. But for the sake of calculations it IS 1 whether you like it or not...sorry... >__>

He is saying that if they where two seperate numbers, you could easily find another number between them. For instance, 0.2 and 0.3 are seperate numbers, and you can fit fractions like 0.27 or 0.296 in between them. But if the number 0.999... is recurring forever, you cannot possibly find a number that is less than 1.0 but greater than 0.999... If you can not find a fraction small enough to fit between the two, one must not be greater than the other. They must therefore be equal.

 

[Zukhramm]

hmm, not sure where you are getting with this post. Ok, 0.9999.... is not 1 in reality. But for the sake of calculations it IS 1 whether you like it or not...sorry... >__>

No. It IS 1. In "reality".

 

[matt87_50]

yes.

every time you add a 9 digit to the end, it gets a closer towards 1.

it 'tends' towards 1

this means in 'infinity' or, when there are infinite 9 digit, it equals one.

for all practical purposes.


note the proofs that say

1/3 = 0.333...
2/3 = 0.666...
so 3/3 = 1 = 0.999...

are pointless...

who the hell says 1/3 = 0.333...

that's no more unquestionable as saying 1 = 0.999...


or think of it this way:

1= 0.9 + 0.1
= 0.99 + 0.01
= 0.999 + 0.001
= 0.9999 + 0.0001
= 0.999... + 0.000...

yes, thats right, there is no '1' after the infinite number of 0 digits.

the (infinite + 1)th digit is not 1.

there is no infinity + 1, infinity + 1 is infinity, and we already said the infinite digit is 0!

...

infinity + any number or 0 is infinity
infinity + infinity is infinity
infinity - infinity is 0

any number except 0, divided by 0, is infinity

infinity divided by infinity is 1

infinity multiplied by any number is infinity

and probably, any number divided by infinity is 0

note that there is negative infinity, and signs work the same way they do with any other number, when doing operations with infinity.

-infinity / infinity = -1 ect...


again, practically speaking...

 

[HeySeansOnline]

Technically yes, but in most situations I'd go with with no.

Here's a hypothetical, an omnipotent figure pops up in front of you and makes you an offer, you can either be extremely rich your entire life, and have a 99.999...% chance of dying, or to make it even worse some sort of death free unthinkable hell, after you take that option. Or you could just walk away, and not die. Basically a 100% chance, of not dying. I would go with option B, because anything is statistically possible unless there is an absolute 100% chance of it not happening, which even then it is arguable that nothing is absolute.

 

[Zukhramm]

who the hell says 1/3 = 0.333...

Who the hell doesn't? The was probably one of the first things I learned about math when I got my hands on a calculator as a small kid.

 

[Winthrop]

x=.9999...
10x=9.9999...
10x-x=9.9999...-.9999...
9x=9
x=1
.9999...=x=1
.9999...=1

The flaw with this is that you have one less than infinity 9s after the decimal in 9.999 so it would not be 9 but 8.999...1

OT they are not equal. The reason they always appear to be is that the difference is so negligible that it can be ignored. You could say .999... &#8776; 1 but that is because it is approximation. Also 1/3 does not equal .333... it is just a common approximation like pi &#8776; 3.14

 

[Floppertje]

christ, can we drop this already? 0.99999999999999999999 is NOT 1 if it were 1, THEY WOULD JUST CALL IT 1!
it's just a teeny tiny bit smaller than one, but it is not one, no matter how many times you do your fancy algebra.
and (9.9999999999-0.99999999999) is NOT 9, it is 8.99999999991

using rounding errors does not make you smart.

 

[Fidelias]

hmm, not sure where you are getting with this post. Ok, 0.9999.... is not 1 in reality. But for the sake of calculations it IS 1 whether you like it or not...sorry... >__>

No. It IS 1. In "reality".

No, it doesn't.

When you see this in a math problem, you must substitute 0.999... for 1 because there is no way to use an infinite number in a math problem. However, as soon as you substitute 0.999... the problem becomes an approximation, because 1 does not equal 0.999 repeating. Look at my post earlier to see what I mean.

 

[karplas]

For me, this thread is not about the mathematics anymore. 0.(9) = 1, you can follow the links previous posters have posted for proofs. There is no room for opinion or 'personal beliefs'.

How do people get the arrogance to answer a resolute 'no', while trained mathematicians have come to the conclusion the answer is 'yes'? I would really like to know what credentials these nay-sayers have.

Sure, the statement 0.(9)=1 might be counterintuitive to some, and I can imagine an appeal to authority is hardly convincing, but rather than coming to the conclusion that 'experts are wrong, I am right', can't one admit one's ignorance and realize that more likely the experts are right and that one lacks the mathematical insight or knowledge required to fully comprehend the proof? Or do we really think that those gifted mathematicians are bigoted when it comes to this issue, or that they are lying to keep the public ignorant and that we, great independent thinkers, should think for ourselves and, despite our lack of expertise, reject their 'ideas'?

Being critical and skeptical, I find, is a good thing. But it's also important to recognize your own ignorance and admit that others are more likely to know better.

I'm sorry if my formulation was somewhat chaotic, or my tone aggressive and condescending, but things like these tend get me a bit annoyed

 

[Hatchet90]

I asked my friends this... and they didn't know what the fuck I was talking about. So thanks, for this thread. I think it's generally accepted that any number divided into itself equals 1.

1/3 = .333....
2/3 = .666....
3/3 = 1

The .9999... stretches on to infinity yes, but, from a logical perspective. One must look at it as 1. Otherwise we'd all go mad. Stop with these math problem threads! You're making me look like a moron.

 

[mps4li3n]

hmm, not sure where you are getting with this post. Ok, 0.9999.... is not 1 in reality. But for the sake of calculations it IS 1 whether you like it or not...sorry... >__>

No. It IS 1. In "reality".

In "reality" infinity might not exist, so 0.(9) would never actually occur... you might just get a number that has so many 9 after zero that you can't possibly count them all before the universe ends... and it would not be 0.(9)... you'd never be able to tell though.

And of course if it does exist there would never be a noticeable difference between it and 1 even if the universe lasted for infinity...

That's why it works even if math proof could be wrong, because there's no way it can affect reality differently then 1 does...

 

[mps4li3n]

the experts are right and that one lacks the mathematical insight or knowledge required to fully comprehend the proof?

The proof is pretty simple, everyone with any math knowledge should understand it...

The problem is that understanding it's real world justification is harder... way i see it is that because the 9 goes on for infinity it would take infinity for .(9) to be different from 1, and because infinity never ends it never is...

So yeah, magic...

 

[Kingsman]

Anyone who says yes to this does not know basic Calculus.

The difference between the limit of something approaching x and the actual value of x REALLY matters at that level.

 

[Spencer Petersen]

Ok take this logic

If you take the limit of y=(1/2)^x where x goes to infinity, you get 0

Logically, it wouldn't matter what fraction was inside the parentheses as long as it was between 1 and 0, y=(.1)^x would work equally as well

Is it not true that .1=.1^1? or .01=.1^2? or .001=.1^3?
Following this pattern, the decimal can be represented as .1^x where x is the number of zeros in between the final digit and the decimal point, minus 1

Now, if I gave you the number .(0)1, where its infinite zeros followed by 1, would it not be represented by the function .1^(&#8734;-1)? Isn't &#8734;-1 the same as &#8734; for the purposes of algebra? So it could also be represented as .1^&#8734;.

Haven't we proven that in a case of finding the limit of y=(.1)^x where x goes to infinity the answer is always 0?

So logically, .(0)1=0.

Now, what is 1-.(0)1?
Wouldn't it be .(9)?
So, .(0)1=0,
1-.(0)1=.(9)
1-0=.(9)
1=.(9)

 

[Zukhramm]

The flaw with this is that you have one less than infinity 9s after the decimal in 9.999 so it would not be 9 but 8.999...1

There's no such thing as "one less than infinity". Either it's infinitely many or there's finite number, which is followed by another finite number and not infinity.

There's yet to be a correct proof from someone who claims they're not the same, and multiple proofs from the ones saying they are. But I guess it's easy to argue you're correct if you ignore proofs.

 

[Winthrop]

snip

The proofs all use rounding errors. I personally know mathematicians who have proven those wrong. for instance 1/3 is not .33333 it is approximate. ((.99...)10)-.99.. = 8.99...1 not 9. I have not seen one of these proofs that does everything correctly. They need an approximation in the equation rather than an equals sign or it fails to be correct, and an approximation would not prove that .99... = 1

 

[The_root_of_all_evil]

Yes, but that is where it deviates from real life.

Actually that is real life. If you're measuring distance up to an infinite point, you can't reach it. That's the point of infinite.

The best way of knowing whether a number can be rational is whether it can be converted to a simple fraction.

Remind me, what is 0.(9) as a fraction? Because 1/3*3 is 1. That's the point of decimalising fractions, or fractionalising decimals, you store the tolerance. Infinitely small measurements are treated as 0, but they still hold measure.

But then, repeated posts on a subject that has an official answer and a differing scientific answer are always good for post boosting. See the Triple Point of Water, How Many Moons does Earth have, Is Pluto a Planet and others.

 

[rutger5000]

Lets give the number you mentioned X. Depends on situation, and of the order of magnitude of 1 - X (the number you gave). In most cases X equals 1 for all intends and purposes if 1 - X is somewhere in the order of magnitude of tenth to the minus 6 power. (1 divided by a million).
For Math, no it doesn't equal math and thats why math suck. Physics is better, and there it can equal one.