07/10/2018, 10:34 PM
(This post was last modified: 07/11/2018, 02:54 AM by sheldonison.)
(07/09/2018, 08:34 PM)Xorter Wrote: Hi!
I agree with Sheldon almost at all. If I were you, I would use the following notations:
Hn(a,b) = a[n]b = H(a,n,b) or the Knuth's uparrows, the second is simplest as I think...
I like the wikipedia hyperoperation definition since it shows the operator sequence. Why is "tet" the 4th operator?
- \( H_0(b)=1+b\; \) successor, which is a unary operation
- \( H_1(a,b)=a+b \)
- \( H_2(a,b)=a\cdot b \)
- \( H_3(a,b)=a\uparrow b=a^b \)
- \( H_4(a,b)=a\uparrow\uparrow b=\text{tet}_a(b) \)
- \( H_5(a,b)=a\uparrow\uparrow\uparrow b=\text{pent}_a(b) \)
- \( \forall n>0\,H_{n}(a,b)=H_{n-1}\left(a,H_{n}(a,b-1)\right) \)
- Sheldon