User blog:Edwin Shade/Just Practice, That's All !

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My Rules for Fixed Points
1.) If there exists a fixed point for the function $$f(x)$$ such that $$x=f(x)$$, then it is also equal to $$f^{\omega}(0)$$.

2.)The second fixed point of the function $$f(x)$$ is $$f^{\omega}(f^{\omega}(0)+1)$$.

3.) $$f^{\omega}(f^{\omega}(0)+1)$$ is always greater than $$f^{\omega}(0)$$.

$$\mho\langle\langle\mathfrak{s}\rangle ,n\rangle$$ means to replicate and concatenate the string of symbols $$\mathfrak{s}$$ a total of $$n$$ times.

$$\langle\mathfrak{s_1}\rangle\ddagger\langle\mathfrak{s_2}\rangle$$ means the concatenation of the strings $$\mathfrak{s_1}$$ and $$\mathfrak{s_2}$$.

Lastly, $$[\mathfrak{s}]\ominus n$$ means the removal of the last $$n$$ elements or numbers in the string $$\mathfrak{s}$$.

Unary and Binary Argument Arrays

$$[0]={^{12}}{12}$$

$$[n+1]=\mho\langle\langle 12\uparrow (\rangle ,12\rangle\; [n]+1\;\mho\langle\langle )\rangle ,12\rangle$$

$$[1,0]=\mho\langle\langle [\rangle ,12\rangle\; 0\;\mho\langle\langle ]\rangle ,12\rangle$$

$$[1,n+1]=\mho\langle\langle [\rangle ,12\rangle\; [1,n]+1\;\mho\langle\langle [\rangle ,12\rangle$$

$$[n+1,0]=\mho\langle\langle [n,\rangle ,12\rangle\; 0\;\mho\langle\langle ]\rangle ,12\rangle$$

Generalized Rules for Polyargumental Arrays

$$[\mathfrak{z},a,\mathfrak{s},b]=[\mathfrak{s}]$$

$$\mathfrak{z}\in\mathbb{P}$$, where $$\mathbb{P}=\{x|(x=\varnothing)\or(x=0)\or(x=\mho\langle\langle 0,\rangle ,y\rangle 0\rangle);y\in\mathbb{N}^+\}$$

$$\mathfrak{s}\in(\mathbb{T}\or\varnothing)$$, where $$\mathbb{T}=\{Z_r|Z_{n+1}=\langle Z_n\rangle\ddagger\langle ,y\mho\langle\langle '\rangle ,n\rangle\rangle ;n\in\mathbb{N}^+;Z_0=y;r\in\mathbb{N};y\and(y\mho\langle\langle '\rangle ,n\rangle)$$

$$\in\mathbb{N}^+\}$$

$$(a\and b)\in\mathbb{N}$$

$$\xi=\varphi(1:\xi)$$, $$\xi=\psi(\Omega^{\Omega^{\Omega}})$$

$$\varphi^{\omega}(1:\psi(\Omega^{\Omega^{\Omega}})+1)>LVO$$

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