User blog:Sait2000/Goodstein Hierarchy

$$R_{a}^{b}(n)=R_{a}^{b}(n,0)$$

$$R_{a}^{b}(0,t)=0$$

$$R_{a}^{b}(n,t)=R_{a}^{b}(\lfloor n/a \rfloor,t+1)+b^{R_{a}^{b}(t,0)}(a-\lfloor n/a \rfloor))$$

$$g_{\alpha,n}(0)=n$$

$$g_{\alpha,n}(m+1)=max(R_{{G_{\alpha}}^{m}(2)}^{{G_{\alpha}}^{m+1}(2)}(g_{\alpha,n}(m)),1)-1$$

$$G_{0}(n)=n+1$$

$$G_{\alpha+1}(n)={G_{\alpha}}^{\mu k(g_{\alpha,n}(k)=0)}(2)$$

$$G_{\alpha}(n)=G_{\alpha \left [ n \right ]}(n)$$