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Topic: Matheology § 430
Replies: 28   Last Post: Feb 12, 2014 4:06 AM

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Posts: 3,394
Registered: 10/18/08
Re: Matheology § 430
Posted: Feb 10, 2014 3:59 AM
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Am Montag, 10. Februar 2014 09:38:24 UTC+1 schrieb
> On Monday, February 10, 2014 10:08:58 AM UTC+2, Virgil wrote:

> The real numbers are not countable because they don't exist.

That depends on the definition. I accept pi or sqrt(17) as real numbers although I know that these numbers cannot be represented but only approximated by strings of digits.

> Here is a proof that D.Cuts do not define irrational numbers:

In my opinion the expression LIM(1 + 1/n)^n defines e. I accept that (although it is impossible to find all digits) because we can calculate the string of digits up to every desired precision eps > 0.

> Now, if you assume that all "real" numbers can be represented as decimals, then I have proved (irrefutably), that the real numbers are indeed countable,

That is certainly correct because the premise is false.

Regards, WM

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