I found the huge number Latri here

If I understand it right, it can be written as

$< 3 , 3 , 3 >$

$< 2 >$

with Bowers 2-dimensional arrays.

Is this correct ?

I wonder where the number

$< 3 , 3 , 3 >$

$< 3 >$

lies in the fast growing hierarchy. It should be VASTLY larger then Latri, but how much larger ?

It must be far below $$f_{\omega^{\omega^2}}(3)$$ which is approximately the magnitude of

$< 3 , 3 , 3 >$

$< 3 , 3 , 3 >$

$< 3 , 3 , 3 >$

Does someone know a good approximation in the fast growing hierarchy ?

## Best Answer

Latri is $\{3,3,3\;(1)\;2\}$ which, as you correctly stated, represents a two-row array with $\{3,3,3\}$ in the first row and a sole $\{2\}$ in the second row.

The second number you've mentioned can be written as $\{3,3,3\;(1)\;3\}$.

In general, $\{a,b,c\;(1)\;x\}$ is in the same ballpark as $f_{\omega^\omega \cdot (x-1)+(c-1)}(b)$ (the value of $a$ doesn't change the final value by much).

So:

$\{3,3,3\;(1)\;2\} \approx f_{\omega^\omega+2}(3)$ (that's the Latri)

$\{3,3,3\;(1)\;3\} \approx f_{\omega^\omega \cdot 2+2}(3)$