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It should be noted that an irrational number is any real number that cannot be expressed as a ratio between two integers. .999.... is a number divisible by 1, 3 and 9. If divided by 9, we get .111...., which is 1/9. So .999....=9*(1/9) (dividing by 3 will give the same results). But numbers must always be looked at in their simplest terms when using theory, so 9*(1/9)=1. The number 1 is not a ratio between two integers (in simplest terms), and therefore .999.... cannot be expressed as a ratio between two integers and is thusly an irrational number. A number cannot exist simultaneously as a rational and irrational number, thus it is not possible for .999.... to equal 1.
Last edited by SeeDRankLou; 05-11-2004 at 05:05 AM.
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