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Mothematician post
(hexbear.net)
Banned? DM Wmill to appeal.
No anti-nautilism posts. See: Eco-fascism Primer
Vaush posts go in the_dunk_tank
Dunk posts in general go in the_dunk_tank, not here
Don't post low-hanging fruit here after it gets removed from the_dunk_tank
\begin{align} 0.999.... &= 9\cdot(0.1+0.01+0.001+... ) \ &= 9\cdot( 0.1^1 + 0.1^2 + 0.1^3 + ... ) \ &= 9\cdot(\sum\limits_{k=1}^\infty ( \frac{1}{10^k} ) ) \ &= 9\cdot(\sum\limits_{k=0}^\infty ( \frac{1}{10^{(k+1)}}))\ &= 9\cdot(\sum\limits_{k=0}^\infty \frac{1}{10}*(\frac{1}{10^k})) \ &= \frac{9}{10}\cdot (\sum\limits_{k=0}^\infty (\frac{1}{10^k})) \ &= \frac{9}{10}\cdot \frac{1}{(1-(\frac{1}{10}))}\ &= \frac{9}{10}\cdot \frac{10}{9} = 1 \end{align}
The crux rests on a handy result on from calculus: the sum of an infinite geometric series looks likes s = 1/(1-r), when s = \sum\limits_k=0^inf r^k, and |r| < 1.
Sorry for the latex. When will hexbear render latex? This is a bit more readable:
(aesthetic edit for our big beautiful complex analysts)
And doesn’t this mean 0.99 approaches 1
A real number can't be approaching anything. It is not a function or any other sort of object that can be said to be approaching anything.
No. 0.99 is 0.9+0.09. The proof I gave shows that 0.99999999999999999999999999999999999(...) is equal to 1.
K