Poll: Does 0.999.. equal 1 ?

[Woodsey]

0.999 = 0.9999999999999...

1.0 = 1

1/3 = 0.3 recurring

0.3 recurring X 3 = 0.9 recurring and 3/3

3/3 = 1

Answer: YEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEES.

Why must you people keep asking?!

From Wikipedia on the subject (and my Dad is a Maths teacher, so I know this paragraph is right anyway):

"The equality 0.999... = 1 has long been accepted by mathematicians and taught in textbooks to students. In the last few decades, researchers of mathematics education have studied the reception of this equality among students, many of whom initially question or reject it. Many are persuaded by an appeal to authority from textbooks and teachers, or by arithmetic reasoning as below to accept that the two are equal. However, some are often uneasy enough that they seek further justification."

 

[veloper]

So many elegant proofs and wasted because the question is flawed. It should say recurring, not just "0,999" which is 0,9990.

the ellipsis indicates recurring

0.(9) is both shorter and clearer.
It would also have ensured fewer bad answers. I can hardly believe the poll would have otherwised turn out that discouraging and with wikipedia only a click away.

wikipedia is not FACT! and I don't think any one was confused by m y question! everybody knew I was talking about reoccurring!
you are the only one that didn't get the question here

Don't worry I got the question and wikipedia is a much, much better source for your math needs than a random forum, trust me.

Wikipedia tends to be an excellent resource for math and computer science concerns. Care should be taken when using it as a resource for information regarding a current situation, or a situation in which there are disputing narratives.

Agreed.

 

[Tharwen]

The only reason people have trouble with it is that you can't easily work with infinity using real numbers.

All of the extra 9's adding to the end means that it tends towards 1, which means that by the time you've gone through an infinite number of iterations, you have 1.

Obviously, we can't do that, so people are just falling back on 'I can't see it so it's wrong'.

 

[Volkov]

thanks ! you can never count on it to be 100% correct tho !

If you have any doubt about a Wikipedia's math article, your only better source will be a direct conversation with an expert in the field. I mean, even bypassing books, because books can also be erroneous (especially on middle school-type stuff, such as the OP question). A thousand forums are not nearly as good as 1 Wikipedia math article. I have no idea why it happens to be this way, but I can tell you that I have a masters degree already, am a doctoral candidate, and still Wikipedia's math articles are an everyday reference for me. (Even if I can't cite them in a paper). Everything else on Wikipedia (except maybe sports statistics) is not remotely as well-written, detailed, or correct.

 

[cahtush]

no, it has to do with that our number system is around 10, if it was for example 6, we wouldnt have this problem.

 

[TilMorrow]

Does 1=0.99999...? No
If you were told to round it up to 1 significant figure then in that case it would be 1.
But straight off does 1=0.99999...? No it doesn't.

 

[Deadyawn]

I said yes. 0.999... is close enough to 1 that it should be allowed the same kind of priviliges and respect. Just because human logic is slightly flawed in this area because our minds cant comprehend infinity doesn't mean that we should discriminate agaisnt 0.999... that would be just unfair. And to all of you who say 0.999... does NOT equal one, your a bunch of capitalist scum sucking pigs! ALL NUMBERS ARE EQUAL!

.....Except for 0. I mean, where does that asshole get off...

 

[Aurgelmir]

0.9999... = 1 Yes
but it does NOT = 1.0000...

1 is a number with a defined decimal places, meaning that it could be anything from 0.5000... to 1.4000... (probably even tighter gaps there but whatever)but it no longer equal those numbers if you add a decimal point...

 

[Bon_Clay]

No, it does not ,never had never will. You need to round it off for it to be equal 1. Else it will be equal 0.99999......

There is no rounding going on. As I explained in my previous post:

Basically if you were rounding, you would be adding a small bit to the 0.999.. to make it fully equal to 1 right? Well that small bit you want to add doesn't exist. Any real number you could possible imagine added to 0.999... would make it a HIGHER number than 1.

0.0...01 doesn't exist. You can never reach the 1 on the end. That digit can and will never come up, and doesn't exist.

Does 1=0.99999...? No
If you were told to round it up to 1 significant figure then in that case it would be 1.
But straight off does 1=0.99999...? No it doesn't.

Wrong, as per above.

 

[The_root_of_all_evil]

Worst. Mathematical. Problem. Ever.

The Agnosticism of Maths.

It's equivalent but not equal.

 

[Sanglyon]

(comment removed by the author)

 

[Damien Granz]

Though my this rationality, every number conceived is the same as every other number, when looked at through the focus of infinity.

.(9)=1 because doing so in any other way forces you to invent new objects or numbering systems.

It's just a quirk in expression, a solution made in convention that makes other solutions work out, not some grand philosophical expression.

 

[Lukeje]

Why do people never accept the most trivial proof?

1 - 0.(9) = 0.(0)1.

Define 0.(0)1 = 0 (as we are working in an Archimedean numbering system).

QED.

People don't seem to understand that it is possible to describe a system where the two aren't equal. It's just more consistent to define infinitesimals as zero than for e.g. 9/9 to be different than 1.

 

[milna64]

Basically, it comes down to the fact that an infinitely small difference is in fact, INFINITELY SMALL! We already have a name for infinitely small. ZERO!

The better question (which has the same answer) is does 0.999...8 = 1?

 

[Lukeje]

Basically, it comes down to the fact that an infinitely small difference is in fact, INFINITELY SMALL! We already have a name for infinitely small. ZERO!

The better question (which has the same answer) is does 0.999...8 = 1?

Ermm... 2*0 also equals 0.

 

[silasbufu]

A bit too many math threads for one day .

Also, you could say it's equivalent. Calling it equal seems just wrong to me.

 

[Drakulea]

No, of course 0.(9) doesn't equal 1. It goes 0.999... to infinity.

Now granted, if you use the value of 0.(9) in real-life applications, you might indeed decide that the approximation error from 0.(9) to 1 is neglijible and just consider it 1.

But from a purely mathematical point of view, no, 0.(9) does NOT equal 1.

EDIT :

Same issue for something that is infinitely small like 0.000000...00001 . Is it equal to zero? No, of course not, it represents a very,very small but non-zero value.

In actual applications would you care that 0.0000....001 is not zero ? Most of the time,no. But it depends on the scale of magnitude of applications.

It all comes down to approximations and how they are relevant to a context.

 

[TiefBlau]

I'v had in-depth conversations about this on many occasion. Just wondering what you guys have to say . . .

I NEED TO KNOW!

Short answer: Yes.

No it doesn't. The gap is so infinitesimal that it hardly counts, but 0.9999 recurring does not equal one.

You're right, in that the gap is infinitesimal. It's infinitely small. So small, that the gap is zero.

Basicly it boils down to limits:

Lim(x)=1 for x->1

It's more like Lim(f(x))=1 for x->k, and we're trying to decide if that means f(k)=1.

Doesn't make a difference though, because there's no real infinitesimal number in our system, and so it must be true.

I'm really sick of this math trends.....keep in mind we made it.

We made math.

However, we did not make logic. Math is our means of understanding it, and it has flaws.

Does 1=0.99999...? No
If you were told to round it up to 1 significant figure then in that case it would be 1.
But straight off does 1=0.99999...? No it doesn't.

Rounding implies that you're adding or taking away something to make it complete. There's nothing to add or take away. If one thing is infinitely similar to another, they're one and the same for the purposes of our number system.

0.9999... = 1 Yes
but it does NOT = 1.0000...

1 is a number with a defined decimal places, meaning that it could be anything from 0.5000... to 1.4000... (probably even tighter gaps there but whatever)but it no longer equal those numbers if you add a decimal point...

Hahawut?

No, of course 0.(9) doesn't equal 1. It goes 0.999... to infinity.

Which can be expressed as 1.

Now granted, if you use the value of 0.(9) in real-life applications, you might indeed decide that the approximation error from 0.(9) to 1 is neglijible and just consider it 1.

The approximation error is zero. It's infinitely small, so small that it's not only negligible, it's just zero.

But from a purely mathematical point of view, no, 0.(9) does NOT equal 1.

No.

 

[Sikachu]

I'v had in-depth conversations about this on many occasion. Just wondering what you guys have to say . . .

I NEED TO KNOW!

If you needed to know so fucking much you probably could have checked some of these threads out rather than reopening this flame war between morons who have a small amount of knowledge of middle-school maths and frustrated intelligent people who've at some point applied their cognitive faculties to the problem. Or perhaps even had a look on wikipedia.

http://www.escapistmagazine.com/forums/read/18.85789-Interesting-fact-0-999-1?page=1
http://www.escapistmagazine.com/forums/read/18.104684-0-99-Repeating-1
http://www.escapistmagazine.com/forums/read/18.144173-Is-1-more-that-one-number

http://en.wikipedia.org/wiki/0.999...

So it becomes pretty clear that it's not that you "need to know" but more that you 'need to create a flame war' probably to garner yourself a badge. This is pathetic.

 

[RhythmStick]

.9 reccuring doesn't even exist, because decimals are fake numbers that represent fractions, and .9_reccuring can't be made with fractions