Re: A question for set-theorists

Op 21/11/2024 om 22:03 schreef joes:

Am Thu, 21 Nov 2024 12:54:22 +0100 schrieb WM:

On 21.11.2024 01:18, joes wrote:

Am Wed, 20 Nov 2024 19:32:38 +0100 schrieb WM:

The density of coloured intervals within the first n intervals is a
sequence converging to zero. Every positive eps is undercut. The limit
cannot be 1.

Formally: lim n->oo n/(2^n) = 0

But you don't believe it?

I don't believe in falsehoods. How do you derive the above? Both the
denominator and numerator diverge. The expression oo/oo is undefined.
 

lim n->oo n/(2^n) = lim n->oo 1/(2^(n-(ln(n)/ln(2)))) = 0
lim n->oo n/(n^3) = lim n->oo 1/n^2 = 0
https://www.desmos.com/calculator/ulookjqjcq
https://www.wolframalpha.com/input?i=lim+n+to+infinity+1%2F%282%5E%28n-%28ln%28n%29%2Fln%282%29%29%29%29