0.99999.... = 1? (2 Viewers)

[klaw]

Why do I get 0.99999.... = 1?
Working out:
let x = 0.999999.....
then 10x = 9.99999.....

10x-x=9
.:x=1

Other way:
0.99999....=9/10+9/10²+9/10³+.......+9/10^infinite
= (9/10(1 - 1/10^infinite))/(1-1/10)
=1

 

[shafqat]

Because it's true.

 

[switchblade87]

Lol, got ya calc on fix mode?

 

[klaw]

Lol, got ya calc on fix mode?

nah... didn't use a calculator, used the working out shown in the original post.

 

[gordo]

therfore

the limit as x -> inf of 1 + (1 x 10^-x)
is the same as the limit as x -> inf of 1 - (1 x 10^-x)

comments?

 

[David_O]

0.9999...
=0.9 + 0.09 + 0.009...
which is a GP with sum 1.

Any two unique numbers, rational OR irrational, must have another rational/irrational number in between them.
No number exists between 0.9999... and 1.
:. 0.9999... = 1

Gordo's:
0.9 = 1 - 10^-1
0.99 = 1 - 10^2
0.9999... = lim x->infinity 1 -10^-x = 1

Consider a square.
Take 9/10 of the area, and repeat.
If done an infinite number of times, the square is completely shaded.

Convinced yet?

 

[Meldrum]

That is why maths is fucked.

Given that 1=2, 1=/=2 and now 0.9*=1; Maths = gay.

 

[withoutaface]

No number exists between .99999999999... and 1, hence they are not distinct numbers, and hence .99999999...=1

 

[gordo]

that might slightly affect the statistics on a colossal amount of discreet data

 

[brett86]

Why do I get 0.99999.... = 1?

although 0.99999... [going on forever] doesnt look like it equals 1, it does for the reason that we can never write down infinity 9's because infinity is a concept and not a value

 

[MajinR]

although 0.99999... [going on forever] doesnt look like it equals 1, it does for the reason that we can never write down infinity 9's because infinity is a concept and not a value

I agree...

i think that technically 0.99999.. will never be the same as 1.0, its just that the more 9s you add, the closer it approaches to 1.

 

[rama_v]

That is why maths is fucked.

Given that 1=2, 1=/=2 and now 0.9*=1; Maths = gay.

1 is not equal to 2, the proof that states this is mathematically incorrect because of division by zero.

 

[withoutaface]

I agree...

i think that technically 0.99999.. will never be the same as 1.0, its just that the more 9s you add, the closer it approaches to 1.

Since you've said it goes to infinity then you've automatically defined it as the limit, and hence equal to one.

 

[KFunk]

That is why maths is fucked.

Given that 1=2, 1=/=2 and now 0.9*=1; Maths = gay.

That is now my new favourite proof.

 

[Dumsum]

This has been the topic of many long and interesting debates in class

 

[hasterz]

this is no more than questions from the yellow fitzpatrick 2 u book.

theres an explanation in that textboook

 

[*Buttercup*]

1 is not equal to 2, the proof that states this is mathematically incorrect because of division by zero.

what is the proof that states it??? ive never seen it

 

[rama_v]

what is the proof that states it??? ive never seen it

Its in this thread, somewhere..

http://community.boredofstudies.org/showthread.php?t=54239

 

[*Buttercup*]

Its in this thread, somewhere..

http://community.boredofstudies.org/showthread.php?t=54239

Thanks (10 char)

 

[adgala]

let n = 0.11... = 1/9
therefore
9n = 0.99... = 9/9 = 1

at least that's what i've been taught