Wondrous patterns, it just so happens that the rules to the Goodstein sequence are pretty much equivalents to Hardy hierarchy :-)
From the Hardy hierarchy, we can build the fast growing hierarchy.
And from there you can reference any notation scheme, such as Conway's chained arrows (which only go up to about $f_{\omega^3}$ as far as I know) or BEAF (Bower's exploding array notation)
From the Hardy hierarchy, we can build the fast growing hierarchy.
And from there you can reference any notation scheme, such as Conway's chained arrows (which only go up to about $f_{\omega^3}$ as far as I know) or BEAF (Bower's exploding array notation)
How can one prove the statement
$$\lim\limits_{x\to 0}\frac{\sin x}x=1$$
without using the Taylor series of $\sin$, $\cos$ and $\tan$? Best would be a geometrical solution.
This is homework. In my math class, we are about to prove that $\sin$ is continuous. We found out, that proving the above s...
Most people assume that 3D models are just a collection of triangles. This is false. They are a collection of one sided triangles. In other words, one side exists but the other does not. This is known as backface culling. I can thereby construct the following geometric puzzle regarding rigid moti...
