Forum:Shrinking hierarchy

A hierarchy that shrinks instead of growing!

$$f_{-1}(n)=n/2$$

$$f_{(\lambda+2)(-1)}(n)=f^n_{(\lambda+1)(-1)}(n)$$

Comparisons:

$$f_{-1}(n) = n/2 $$

$$f_{-1}(f_{-1}(n)) = n/4 $$

$$f_{-2}(n) = n/2^n $$

$$f_{-2}(f_{-2}(n)) = n/2^{n}*2^{n} = n/4^{n}  $$

$$f_{-3}(n) = {n/(2^n)^{n}} = n/2^{n^2} $$

$$f_{-3}(f_{-3}(n)) = n/2^{n^2*2} $$

$$f_{-4}(n) = n/2^{n^3} $$ $$f_{(\lambda+1)(-1)}(n) = n/2^{n^\lambda} $$

It only works up to $$\lambda < \omega$$ : since theres no such thing as a negative limit ordinal... or is there?

Chronolegends (talk) 09:22, February 11, 2017 (UTC)