Poll: Does 0.999.. equal 1 ?

[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

 

[pliusmannn]

No, and yes, there is few mathematical views, in physics if small difference matters then you need not to equalise even the smallest of differences and write those, if differences that small doesn't change the result then yes it's =1, in logical way 1 is a whole and 0.(9) is not whole it lacks, correct answer lim(x)= x->1

 

[Sikachu]

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

Yes it can. 1/1.

 

[TiefBlau]

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

Incorrect.

Decimals don't represent fractions; they represent bases of ten. Each digit place is a base of ten, and it's no different when it's behind or in front of a point. Just as 1000 is 10^3, so too is 1 a representation of 10^0, and 0.001 a representation of 10^(-3).

So yes, 0.9 repeated does exist, and it's represented in fraction/whole number form as 1, 3/3, 4/4, 923/923, or whatever you'd like.

 

[Bobbity]

Essentially, because there's an infinitely recurring number involved, then yes.

Besides which, my calculator says so.

 

[USSR]

I'm sorry, but go ask a mathematician.

Damn near everyone on here is an asshole/claims to be a mathematician/an all knowing god.

Please have a mod close this thread. It's only brought flaming, and little discussion.
The most it brings out is "NO, I'M RIGHT!"

 

[MrGalactus]

Mathematically, no, but who cares enough to be that pedantic about it? It's close enough. 1 it is.

 

[VulakAerr]

*snip*
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.

No, it doesn't. It has NOTHING to do with the scale of magnitude. If you are working at the scale of sub-atomic particles, 0.(0)1 is still 0. I mean, fuck it, it could be 0.(0)675 it would still be 0. Because that (0) is an infinite number of zeros means that any number that follows it is irrelevant. 0.99 recurring doesn't mean "a whole lot of nines", it means "nines to infinite", just as "0.00 recurring 1" doesn't mean "quite a few zeros and then a one", it means "an infinite number of zeros". There is literally zero meaning to that number that comes after the zeros. It is not an approximation. It is zero.

 

[mattsipple4000]

is 1.999(reoccurring) 2 ?

 

[Rafael Dera]

As has been said ad nauseam:
1/3= 0.333...
0.333...*3=0.999...
and 1/3*3=3/3=1.
Therefore, 0.999... = 1.
people who say it's infinitesimally smaller are wrong. Why are they wrong? See above.
No maths exprert, and there are probably more rigorous/elegant proofs but this gets the point across imho.

 

[Kinguendo]

Yes, some people have trouble understanding this so I explain it like this...

0.999(r) has no knowable end so think of it as taking a piece of pie away each time and every 9 represents another piece taken, eventually you will have eaten every single piece of that pie no matter how small thus you have eaten 1 whole pie.

 

[Level 7 Dragon]

1/3 = 0.333...
0.333...*3= 0.999...

on a different calculator

1/3 = 0.333...
0.333...*3= 1

Mathematics is flawed

WRONG!

0.3333....=0.3+0.03+0.003+...=

=3(0.1+0.01+0.001+...)=

=3(1:10 [b1] + 1:100 [b2] + 1:1000 [b3]...)=

3x([b1]:1-q)= 3x (1:10) : (1-10)=

=3x 1:10 x 10:9= 1:3

1:3 is not equal to 0.3333.. like we used to, for real we just adapt to make math easier.

:3

 

[Torrasque]

No, they are not the same.
Yes, math is flawed.
You can see this especially in fractions.

disclaimer: fractions are a poor representation of non-fractions
1/2 = 0.5
1/4 = 0.25
1/3 = 0.333...
2/3 = 0/666...

The simple fact that it repeats forever and ever, means one thing: that it repeats forever.
Just like Pi does not exactly equal 3.14, it equals 3.14159265358979323846264338327950288419716939937510582097494459... and then mathematicians throw their hands up in the air, and say it equals 3.14 for the sake of sanity.

To put this into perspective, lets say you live on Earth, and I live 3 light years away.
That is an extremely long ways away, and only an idiot would say that I am touching you.
One day, I decide to teleport back to Earth to visit you, and teleport within 1 centimeter of you.
Compared to the ridiculous distance that separated us before, I am practically touching you. But I am not.
I move to within 1 nanometre of you, just because I am creepy that way, but do not touch you.

Think of 0.999... as that. The difference between 0.999... and 1 is so insignificantly small that depending on the case, you'd just ignore it. But there is still a difference between touching you, and not touching you, whether that is 3 light years, or 1 nanometre.

 

[RhythmStick]

what's 1/9 as a decimal?
what's 9/9 as a decimal?
what's 1/9 * 9 as a decimal?
.(9) equals 1 because it doesn't even exist

 

[mattsipple4000]

Yes, some people have trouble understanding this so I explain it like this...

0.999(r) has no knowable end so think of it as taking a piece of pie away each time and every 9 represents another piece taken, eventually you will have eaten every single piece of that pie no matter how small thus you have eaten 1 whole pie.

when will eventually come ??? do you have a reoccurring pie?

 

[mattsipple4000]

No, they are not the same.
Yes, math is flawed.
You can see this especially in fractions.

disclaimer: fractions are a poor representation of non-fractions
1/2 = 0.5
1/4 = 0.25
1/3 = 0.333...
2/3 = 0/666...

The simple fact that it repeats forever and ever, means one thing: that it repeats forever.
Just like Pi does not exactly equal 3.14, it equals 3.14159265358979323846264338327950288419716939937510582097494459... and then mathematicians throw their hands up in the air, and say it equals 3.14 for the sake of sanity.

To put this into perspective, lets say you live on Earth, and I live 3 light years away.
That is an extremely long ways away, and only an idiot would say that I am touching you.
One day, I decide to teleport back to Earth to visit you, and teleport within 1 centimeter of you.
Compared to the ridiculous distance that separated us before, I am practically touching you. But I am not.
I move to within 1 nanometre of you, just because I am creepy that way, but do not touch you.

Think of 0.999... as that. The difference between 0.999... and 1 is so insignificantly small that depending on the case, you'd just ignore it. But there is still a difference between touching you, and not touching you, whether that is 3 light years, or 1 nanometre.

I like you !! and have been trying so hard to explain this ! thank you

 

[tris4992]

from a objective point of vieuw 0.999... /= 1 in the same way 2/=1
They are two different numbers. The only way they can be equal is if you take rounding into account as 0,999... will always get rounded up to 1 in that case.