05/07/2010, 03:17 AM

(05/01/2010, 11:56 AM)mike3 Wrote: It would be interesting to determine what the upper bound of the regular interval for the bases of pentation would be. We know that for tetration it is , but what about pentation? (I suppose this would require tetration for b greater than to investigate, though, so we'd need other methods like the Abel iteration or the continuum sum (I'm a big fan of continuum sums, by the way ))

I think I finally understand what you're talking about here. There is an interval that plays the same role in pentation as plays in tetration. I talked about the upper bound of this interval here, but whether or not there is a lower bound to this interval is unknown.

Just as the point is the "highest" point on the graph of ,

so is the "highest" point on the graph of .