0.999999 = 1

[SaoKill]

It was a featured article on Wikipedia...
some views:

I. 1 - 0,9999...
0,9 < 0.9999...
1 - 0,9 > 1 - 0,9999...
0,1 > 1 - 0,9999...
similarly: 0,99 < 0,999...
so: 1 - 0,99 > 1 - 0,999...
-0,1 > 1 - 0,999...
You can realise that 1 - 0,999.. is always smaller than 0,0000001 , 0,00000000001 etc. so 1 -0,99999... equal 0, so 0,999... = 1

II. .9 recurring = infinity

III. 0.9 recurring does equal 1, there is no rounding involved.

Take x = 0.9 recurring Multiply by 10 on both sides

10x = 9.9 recurring Minus x from both sides

9x = 9 (since 9.9 recurring - 0.9 recurring (x) = 9)

x = 1 = 0.9 recurring.

IV. 1/3 = 0.33333.... 3/3 = 0.99999999... = 1

[San]

the only one that really made sense to me was the 1/3=.33 recurring 3/3=.999 recurring=1
(IV)

[SaoKill]

explain or learn math and logic?

[Reise]

lol Why can't 0.9 repeating just equal 0.9 repeating?

0.9 would be less than 0.9 repeating though.

[San]

explain or learn math and logic?

are u saying im stupid for not understanding the others

and i can explain it:
technically, 1/3=.333 recurring, therefore 3*1/3 would have to equal .9999 recurring. However, 3/3 is also supposed to equal one, since thats how fractions are . Therefore speaking, .9999 recurring would have to equal 1 through this theory

dont tell me to learn math and logic

[Sharp324]

lol Why can't 0.9 repeating just equal 0.9 repeating?

0.9 would be less than 0.9 repeating though.

Yeah i don't see why this is surprising

[SaoKill]

But through other theories, it doesn't... For example,
0.9 recurring will NEVER equal one, no matter how many 9's you add. It just all depends on how you look at it.

You didn't understand the other views of this topic, so what am I supposed to do? Give you a cookie?

[Sharp324]

But through other theories, it doesn't... For example,
0.9 recurring will NEVER equal one, no matter how many 9's you add. It just all depends on how you look at it.

You didn't understand the other views of this topic, so what am I supposed to do? Give you a cookie?

Wouldn't that be common sense?

[Casey613]

this is second grade shit... seriously >.>

lim(m->oo)+(n=1)^m(9)/(10^n)=1

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

[SaoKill]

Anything wrong with common sense?

[Reise]

Well, 0.9 repeating till infinity you're right will never equal 1. The decimals will get incomprehensibly small but they'll still be less than 1. 0.9 repeating can't equal infinity though, the space between it and 1 would just be reeeeeeeeally minute. Infinitely minute... lol

I'm not sure you should even consider a repeating decimal an "actual" number. That's why we have rounding, but I guess that's why people are confuzzled.

0.3 repeating should round to 0.4 or 0.34 or whatever you want depending on what accuracy you want. I think that's really the case, how accurate you want your solution.

[SaoKill]

Well, 0.9 repeating till infinity you're right will never equal 1. The decimals will get incomprehensibly small but they'll still be less than 1. 0.9 repeating can't equal infinity though, the space between it and 1 would just be reeeeeeeeally minute. Infinitely minute... lol

I'm not sure you should even consider a repeating decimal an "actual" number. That's why we have rounding, but I guess that's why people are confuzzled.

0.3 repeating should round to 0.4 or 0.34 or whatever you want depending on what accuracy you want. I think that's really the case, how accurate you want your solution.

Than the space between infinity and one would only be one too right?

[Reise]

Well, 0.9 repeating till infinity you're right will never equal 1. The decimals will get incomprehensibly small but they'll still be less than 1. 0.9 repeating can't equal infinity though, the space between it and 1 would just be reeeeeeeeally minute. Infinitely minute... lol

I'm not sure you should even consider a repeating decimal an "actual" number. That's why we have rounding, but I guess that's why people are confuzzled.

0.3 repeating should round to 0.4 or 0.34 or whatever you want depending on what accuracy you want. I think that's really the case, how accurate you want your solution.

Than the space between infinity and one would only be one too right?

Nah I think it would be an equally infinite fraction. If you're going to have a difference that's infinitely small, that's exactly what it should be. How you would physically measure that lol, I dunno.

[SaoKill]

I actually meant the space between infinity and one and infinity is only one right? *My mistake

[Reise]

Well it can't be 1 since 1 is bigger than 0.9 repeating lol. This is the kind of stuff that blows up computers.

[SaoKill]

lolers, its how you view it! Thats why I think its a good discussion =P{

[heroo]

this is second grade shit... seriously >.>

lim(m->oo)+(n=1)^m(9)/(10^n)=1

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

not correct, it depends how many '999999' are behind the dot.

if it's infinite, there's no solution.

[slytther]

no flaming but...who cares xD

[IguanaRampage]

That is correct. .99... is not "a really long number that rounds to one for convenience." It is simply 1. ^^

[SaoKill]

Prove it?

[Vindicator]

this is second grade shit... seriously >.>

lim(m->oo)+(n=1)^m(9)/(10^n)=1

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

wrong. Actually, the math is totally right, but that doesnt prove x=1. That proves that you move along the number field through .9 repeating, you are always approaching 1, however, one is never reached.

[-Evan]

I thought we already have a thread for this topic... where NuclearSilo and some other "math" geeks are arguing till death.

[IguanaRampage]

Prove it?

The way I think of it is that I can't picture it. Rather, that infinity is a concept not in my grasp of mathematics, and I doubt it's really in anyone's, because it's so tough to comprehend. So you know that when .99 repeats, the only way to express that in a way that I can really understand is 1. It's not close to 1, since you can't actually express how close it really is. In our system, it's 1. That's how I think of it lol.

[SaoKill]

Thats no logical way to explain it...

In our system, its 1

.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

Would never equal one if you look at it in a simple way.