Recent content by bjshnog

I thought about it a bit and it would be impossible to write an endless string of functions and not have a ##z## sitting around in the result. It must use a limit, as in the second definition. Here's Graham's number. ##G=\Omega_{1}^{64}[{3}\uparrow^{z}{3}]_{z}^{i}(4)##

I see. I have to say the main reason was because I went to the effort to invent something that I didn't think anyone had bothered doing in the past so that I could experiment with it, and I didn't want to be unoriginal. I posted about it here about 3 years ago, but I was bad at organization and...

I've looked around on the internet a bunch, for a standard way to write an arbitrary number of nested functions (eg. ##{f_1}\circ{f_2}\circ\cdots\circ{f_n}##) without ellipses and with a second input variable (eg. the i in ##f_i##), but never found anything. If anyone does this, what is the...

u = unit of distance. Take a solid cube of dimensions (1u,1u,1u) with center at (0,0,0). Cut it straight along x, y and z three times with a circle of diameter 1u parallel to the faces of the cube with the center of the circle at (x,0,0), (0,y,0), (0,0,z) respectively, removing the "shavings"...

I actually began thinking about non-computable numbers, so I Googled it and found Ω. That is what led me to post here, to see if anyone knew of any other non-computable numbers with known properties.

Interesting. Just out of curiosity, is there a standard symbol for the "set of everything" or "set of all numbers"?

Is there any way to prove that a real number exists which is not calculable by any method? For example, you could have known irrational and/or transcendental numbers like e or π. You could have e^x where x is any calculable number, whether it be by infinite series with hyperbolic/normal...

This is incorrect; made correction: \underset{n}{\underbrace {\int \cdots \int }}\left ( \sum_{i=1}^{\infty}\left ( a_ix^{b_i} \right ) \right ) dx^n = \sum_{i=1}^{\infty}\left ( \frac{a_ix^{b_i+n}}{\prod_{j=b_i}^{b_i+n-1}\left ( j \right )} \right ) + \sum_{i=1}^{n}\left (...

\underset{n}{\underbrace {\int \cdots \int }}\left ( \sum_{i=1}^{\infty}\left ( a_ix^{b_i} \right ) \right ) dx^n = \sum_{i=1}^{\infty}\left ( \frac{a_ix^{b_i-n}}{\prod_{j=b_i}^{b_i+n-1}\left ( j \right )} \right ) + \sum_{i=1}^{n}\left ( \frac{c_ix^{n-i}}{(n-i)!} \right ) This is somewhat...

Sometimes I like to find patterns in certain functions, for example, repeated Sigma (Summation) notation. But what if I wanted to do an arbitrary number of nested summations? Or something similar with other functions? Is there a compressed way of writing this? For example: \sum_{k_5=1}^{1}...