Proof that 0.999r=1

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.

 

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.

 

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.

 

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?

 

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.

 

yes it is pretty amazing nice job

 

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

 

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

 

9x= 0.99999999999 (times) 9

 

Agreed.

 

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

 

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.

 

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

 

youre retarded

 

.333 itself, is rounded to 1/3

 

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

 

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

 

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

 

.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.

 

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.