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."
Logically speaking, ((x * 10) - x)/9 should equal x again.
And it does. In the proof that I showed, x = 0.9999... and x = 1. The argument is that both are therefore the same.
Please don't make a mockery of mathematics.
I assure you that I am doing nothing of the sort. Mathematics is based upon proof, not intuition. What I posted was one such proof, there are many others. If you disagree, then please argue with a counter-proof. This particular case is believed by many professional mathematicians themselves, who I would assume know more than you and I about the 'rules of Mathematics'.
Finally, I would request that we please stay respectful. This is posted in the 'puzzles and humour' section and it isn't to be taken too seriously.
Regards
"I spent thirty years learning manners, and I spent twenty years learning knowledge."
I don't think this is making a mockery out of it. Some advanced math classes even study these false proofs. If anything, they help people have a better understanding of math, or in this case a better understanding of the problems with working with infinity.
Edit: I see I was to late with my reply, just ignore then ^_^
Again the same problem as before.
With a finite number of factors we would get:
0.99999 + 0.11111 = 1.11110
1.11110 = 1 + 0.11110
The problem lies with this axiom:
∞+1=∞
So that means that 1.1111... - 0.0000...1 = 1.1111...
The numbers are only equal because the difference is ignored next to infinity. Remember: infinity is not a number, its' a concept.
Last edited by Abdul Fattah; 06-15-2008 at 04:59 PM.
I agree with you that inifinity is what poses the problem here. But Akhee, you are speaking of infinity as though it is a number when it isn't. It is a concept, not a quantity!
EDIT: Ok, never mind.
"I spent thirty years learning manners, and I spent twenty years learning knowledge."
I agree with you that inifinity is what poses the problem here. But Akhee, you are speaking of infinity as though it is a number when it isn't. It is a concept, not a quantity!
EDIT: Ok, never mind.
It seems I edited my post just a few minutes before you were able to make yours
Anyway, on another note, irrational numbers really are irrational in the sense that they aren't necessarily real quantities either! In math we can have infinite terms in an irrational number. Like we can divide the number 1 by the the number two an infinite number of times.
1/2=0.5
0.5/2=0.25
0.25/2=0.125
...
But is that realistic? Say we have a lump of clay, can we divide that into two smaller lumps an infinite number of times? eventually you'll be dividing molecules, atoms, quarks, strings? Is there any guarantee you can repeat this division infinitely? So you could say numbers which are infinitely small or have infinitely small parts (like 1.11111... ) are also concepts rather then quantities just as we both pointed out is the case with infinity itself. This again shows the problem with these proofs, the calculations used treat the irrational numbers like rational numbers.
the calculations used treat the irrational numbers like rational numbers.
Very good point! I agree with your post. Also on a more general level, more often than not, theory differs from reality anyway.
I love to tease people with this. It's so funny seeing my brother know full well that 0.999... and 1 are different numbers but not being able to prove it.
I get a sick sense of pleasure out of it. Maybe I need to get my head checked.
Last edited by Uthman; 06-18-2008 at 12:05 PM.
"I spent thirty years learning manners, and I spent twenty years learning knowledge."
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"0.9999..." = 1 (OP)
Finally, I would request that we please stay respectful. This is posted in the 'puzzles and humour' section and it isn't to be taken too seriously.
Anybody got a problem with that?
Also on a more general level, more often than not, theory differs from reality anyway.
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