I hope this hasn't been posted before. I just wondered how many of you know that the decimal number 0.9999...(recurring) actually equals 1.
Allow me to prove it for you:
Let x = 0.9999... Multiply both sides by ten: 10x = 9.9999... Subtract x from both sides: 10x - x = 9.9999... - 0.9999...
9x = 9.0000... Divide by nine: x = 1.0000...
Anybody want to challenge me on this? Or perhaps somebody would like to post a different proof or counter-proof?
Last edited by Uthman; 06-17-2008 at 07:28 PM.
"I spent thirty years learning manners, and I spent twenty years learning knowledge."
I hope this hasn't been posted before. I just wondered how many of you know of the fact that the decimal number 0.9999...(recurring) actually equals 1.
Allow me to prove it for you:
Let x = 0.9999... Multiply both sides by ten: 10x = 9.9999... Subtract x from both sides: 10x - x = 9.9999... - 0.9999...
9x = 9.0000... Divide by nine: x = 1.0000...
Anybody want to challenge me on this? Or perhaps somebody would like to post a different proof or counter-proof?
Let
x = 0.9999...
Multiply both sides by ten:
10x = 9.9999...
Subtract x from both sides:
10x - x = 9.9999... - 0.9999... <-- You subtracted x on one side, and .999 on the other so it doesn't make sense.
Since 0.3333 + 0.3333 ) 0.3333.. = 0.999..
and since 0.333.. is 1/3, then 1/3 + 1/3 + 1/3 = 1
I hope this hasn't been posted before. I just wondered how many of you know of the fact that the decimal number 0.9999...(recurring) actually equals 1.
Allow me to prove it for you:
Let x = 0.9999... Multiply both sides by ten: 10x = 9.9999... Subtract x from both sides: 10x - x = 9.9999... - 0.9999...
9x = 9.0000... Divide by nine: x = 1.0000...
Anybody want to challenge me on this? Or perhaps somebody would like to post a different proof or counter-proof?
The problem is the surrealism of infinity. In the real world where infinity doesn't exist, then in step 3 where you subtract x, there you'll see that the 9.999... always has one decimal less behind the point than 0.9999...
That way the subtractions can never become 9. So the calculations themself are fine, it's the mathematical axiom of infinity that is dodgy.
The same happens for 1/3 = 0.333... that only works with an infinite number of factors. In reality it's impossible to calculate with that, so we calculate in approximations (so does your calculator).
Last edited by Abdul Fattah; 06-14-2008 at 10:49 AM.
Yes, but remember that the 0.999... is a recurring decimal with an infinite number of nines. For this reason, 1 - 0.9999.... would result in 0.0000000......
There would be an infinite number of zero's in the answer so there would be no 1 at the end because there is no end!
"I spent thirty years learning manners, and I spent twenty years learning knowledge."
I hope this hasn't been posted before. I just wondered how many of you know of the fact that the decimal number 0.9999...(recurring) actually equals 1.
Allow me to prove it for you:
Let x = 0.9999... Multiply both sides by ten: 10x = 9.9999... Subtract x from both sides: 10x - x = 9.9999... - 0.9999...
9x = 9.0000... Divide by nine: x = 1.0000...
Anybody want to challenge me on this? Or perhaps somebody would like to post a different proof or counter-proof?
Who ever showed you that needs to get a good smack in the head.
I suggest you go to a good math teacher and allow them to properly educate you on the rules of mathematics.
Your "equation" boils down to ((x * 10) - x)/9 = something
You've allowed x to be an irrational number, which is fine, but that's where you are having difficulties. Logically speaking, ((x * 10) - x)/9 should equal x again.
Try .888888888 and see what you get with your logic.
(0.888888888..... * 10 - 0.888888888..... )/8 = ?
(8.888888888..... - 0.888888888..... )/8 = What do you think it should be?
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