Proof that 0.999r=1

[ironblade87]

x = .999
10x = 9.99
9x = 8.991
x = .999
.999 = .999

perhaps you should have read my post above; when he states x = 0.999, he means 0.999 to be 0.99999999999999999999999999999999999999999999999999999999999999999 recurring, not just 0.999.

 

[Runescape_Mod]

yeah but perhaps you should know that even if it is recurring... you cannot do what he is saying. if x = 0.99999999999999999 then 10x will have one less 9 after the decimal point. 0.999r =/= 1. It is infinitely close, but it does not equal 1.

 

[ilikepie1]

/Sigh

He made a point to mention that he is using 0.999 recurring,

As for the math, I can't see any problem with it, except that rather than proving 0.999=1, it probably proves recurring numbers are inaccurately portrayed in current mathematics (or maybe that infinity is, in fact a number, so moving the decimal point to the left actually changes the number of 9s after the decimal point from infinity to infinity minus one. I'm not going to try it, but maybe that would make x=0.999). Anyways, the point is that working with things that we don't fully understand, such as infinity, can't deliver conclusive evidence, mostly that which disputes the very core of math. Next thing you know, someone will prove right angles are not congruent by using string theory.

I know that. I just used 0.999 as an example. No matter how many 9's are after a decimal, it still does not equal 1. It get's very close, but not close enough to make them equal.

 

[Cfrey]

Algebra Proof
In this proof, X will equal 0.999. When a number in decimal notation is multiplied by 10, the digits in that number will not change. Instead, the decimal separator (.) moves one place to the right. So 10*0.999=9.999.

X=0.999
10X=9.999
9X=9.999-0.999=9
X=1
0.999=1

The above proof using algebra already is proof that 0.999 can resemble 1.

Uh wrong???

x=.999
10x=9.999
9x=9.999-.999=9
x=.999
.999=.999

x=1
10x=10
9x=9-1=8
x=1
1=1

Where in the world did you come up with this 1?

 

[normalcy]

9X doesn't equal 9. Nine times .9 repeating cannot be exactly nine so therefore X does not equal 1. In other words .9 repeating does not equal one. It's only obvious to start with but you wanted to make it difficult with equations.

 

[ohno2012]

yes it is pretty amazing nice job

 

[ironblade87]

Does anyone on this thread even understand limits? -_-;;;

 

[Guineapigcal]

9x = 8.9999999999999999999999999999999999(insert infinite 9s here)1
Not 9. That's just silly.

 

[Tapeworm]

9x= 0.99999999999 (times) 9

 

[ohnoresident]

Yall just confused the hell out of me.

Agreed.

 

Does anyone on this thread even understand limits? -_-;;;

Considering most users are 13-15, I doubt they do.

 

[Surround Sound]

Yes, it does. They represent the exact same thing.

I remember a teacher explaining it a few years ago, I'll try to show you here.

1/3 = .333... right?
and 1/3 + 1/3 + 1/3 = 1
since 1/3 = .333...
it stands that .333... + .333... + .333... = 1
if you simplify the left half of that equation
you get .999... = 1


There are many more ways to demonstrate this though, that's just one of the simplest to understand imo.

1/3 = 0.333 etc.
3 x 1/3 = 1
Therefore 1 = 0.333 etc. x 3
1 = 0.999 etc.

Exactly what my maths teacher taught me as well.

I think it's definitely a rational theory, but there are flaws.

I'll stick with them being different numbers.

 

[FaTaL Sh0t X]

1=1, 2=2, 3=3... Can't change this shit.

 

[Eric]

youre retarded

 

[distracted]

1/3 = 0.333 etc.
3 x 1/3 = 1
Therefore 1 = 0.333 etc. x 3
1 = 0.999 etc.

Exactly what my maths teacher taught me as well.

I think it's definitely a rational theory, but there are flaws.

I'll stick with them being different numbers.

.333 itself, is rounded to 1/3

 

[Jimmy]

Uh wrong???

x=.999
10x=9.999
9x=9.999-.999=9
x=.999
.999=.999

x=1
10x=10
9x=9-1=8
x=1
1=1

Where in the world did you come up with this 1?

1/9 = .1r
9(1/9) = 9(.1r)
1 = .9r

 

[Obby_Maul]

Yes, it does. They represent the exact same thing.

I remember a teacher explaining it a few years ago, I'll try to show you here.

1/3 = .333... right?
and 1/3 + 1/3 + 1/3 = 1
since 1/3 = .333...
it stands that .333... + .333... + .333... = 1
if you simplify the left half of that equation
you get .999... = 1


There are many more ways to demonstrate this though, that's just one of the simplest to understand imo.

ahh. i'm in algerbra 1 so i was like, WUT o.o till i saw this. i get it now, sort of.

 

[The Real Kurt]

Very interesting, I got into an argument with my math teacher over this lol.

 

[awesome11]

.999999999-repeating DOES equal one, and if u guys somehow don't think that, heres a very quick an easy explanation :
1/3 = .3333
2/3=.66666
3/3= 1!!!!!
IF U MULTIPLY .333333 BY 3, ULL GET .9999, but if u multiply 1/3 by 3, it will equal one.

that is why .9999- equals 1.

 

[hybanks2000]

No. Mathamitically speaking, they are not the same value, and hence, not truely the same amount. The differeance between the two ammounts is infinitly small, and can not be truely understood, only accepted as existing, but the differance still remains.

And Yes. For any real use, they are exactly the same, you would never nitpick over a differance of that infinitly small space between the two values.

So technically no, but in the working world, yes, they're the same bloody number.