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1 != 1


pgrmdave

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for any number x, x = x - .0000...x, i.e. 1 = .9999....9

 

The idea goes like this: .333333...3 = 1/3

*3 = *3

.999999...9 = 3/3 = 1

 

But if this is true, it can be nested, (x - .000...x ) - .0000...(x-.000...x) and so on, to infinity. If taken to infinity, then you are able to subtact an infinite amount from any number and still have a number equal to the origional number. Am I wrong, or is this a big flaw with our number system.

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I agree, it's like if you substract an infinity of times 0.

Your reasoning works if you see the 3.3333333 with a finite number of 3 or .000000....x with a finite number of 0. But your first reasonig doesn't work because 0.33333 != 1/3 (I learned something I also thought it meant factorial, the oposite of your thinking I know this expression of C++, but never would have thought that somebody would use it like that).

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As Tim putted it 0.3333333...3333 --> 1/3, but it will always be different, you will never have equality this is the definition of limit.

I stated that 0.3333!= 1/3, which is not amazing.

 

To explain my self better your theory works only if you start with an infinite numbers of 3, if you write 0.333....33 it may be huge, but it's not infinite and the most important step in your demonstrationis then wrong, because0.3333333....333!=1/3

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