2006-11-22 18:47:17 · 19 answers · asked by navratna s 1 in Science & Mathematics ➔ Mathematics
Surprisingly, yes. This bugged the heck out of me in middle school, but it's a consequence of the way infinity works.
The classic proof is:
x = 0.999999....
10x = 9.999999....
Subtract the first line from the second, and you get
9x = 9, therefore x = 1.
2006-11-22 18:50:23 · answer #1 · answered by Jim Burnell 6 · 2⤊ 1⤋
Yes, without any rounding or limits (limits apply to a series, not a single number) because of the proof mentioned above.
Also this one:
1 / 3 = 0.333...
(1 / 3) * 3 = (0.333...) * 3
1 = 0.999...
The site linked below give several other, irrefutable examples.
2006-11-23 02:57:30 · answer #2 · answered by maradonxp 2 · 1⤊ 0⤋
Yes
2006-11-23 06:03:17 · answer #3 · answered by amit 1 · 0⤊ 0⤋
Yes
2006-11-23 02:58:01 · answer #4 · answered by Asim_ISB 2 · 0⤊ 0⤋
No. It can not be equal to 1. In fact, 0.9999999..... (goes forever) is equal to 10/11 and it is 1/11 less than 1. Therefore, we can write, 1 - 1/11= 10/11 = 0.99999999.......(goes forever).
2006-11-23 03:39:25 · answer #5 · answered by badalde66 1 · 0⤊ 3⤋
Yes it is.
Say x = .999999.....
then 10 x = 9.9999.....
Subtract 2nd from 1st
9 x = 9
implies x = 1.
One more School of thought...
1/9 is 0.111111.......
That makes on multiplication with 9 on both sides...
.9999........ is 1/9 *9 i.e. 1
This is a very famous problem.... But it is equal to one....
Enjoy!!!
2006-11-23 04:58:15 · answer #6 · answered by Shashank B 2 · 1⤊ 0⤋
we can say two numbers are not equal to each other if we can find a distinct real number in between them.
between 0.99999... and 1 there is no real number, as the number 0.99999..... reaches closer to 1 than any other possible number.
So essentially it is equal to 1
2006-11-23 05:40:36 · answer #7 · answered by astrokid 4 · 1⤊ 0⤋
This is a pretty famous question, and there are many ways to prove it. See below for some links to information about it:
2006-11-23 03:21:11 · answer #8 · answered by Kylie 3 · 1⤊ 0⤋
Perhaps sadly, yes.
You need to consider a fraction that generates 0.9999999....ad inf
1/3 = 0.3333....ad inf. is one third the required amount, no tricks.
multiplying both sides by 3 gives,
0.9999....ad inf. = 1
2006-11-23 04:58:24 · answer #9 · answered by yasiru89 6 · 0⤊ 0⤋
Yes, when converting to a fraction. This is one of the few inconsistencies in mathematics.
2006-11-23 09:37:27 · answer #10 · answered by Joel O 1 · 0⤊ 1⤋