Re: A Basic Theorem
- From: gerben47@xxxxxxxxxxx
- Date: 27 Jan 2006 06:25:34 -0800
TheNakedOne schrieb:
> .3 repeated = 1/3
> 3(.3 repeated) = 1
> 3(.333 repeated)=1
> .999 repeated=1
> .9 repeated=1
> Q.E.D.
> Hey everyone, I'm new to sci.math, and this is a proof I gave to many
> teachers at my school, yet none of them could give me a clear enough
> reason as to why this was incorrect. My personal belief is that because
> the repeated (sorry, I couldn't find a superline key) sign means the
> task is being done an infinite number of times, then it actually
> reaches the number which can not be reached in decimal form. I wanted
> to know your thoughts.
>
> Matt
You are correct. To see that the numbers are the same consider x to be
the difference between 0.9999... and 1. If two numbers are different
there is a finite difference between them. In this case, whatever
positive value of x you choose, the difference between 0.999... and 1
will be smaller.
Conclusion: They are the same number!
Gerben
.
- References:
- A Basic Theorem
- From: TheNakedOne
- A Basic Theorem
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