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Base -1
#1
Tetration base 1 is a constant function equal to 1, for x>-1, and has a discontinuity at -1. Or at least that's the solution if .

[Image: 3ZQkL3L.jpg?1]

The oscillatory behavior of bases 0<b<1 suggest that base 0 looks like this on the limit for b=0:

[Image: ToRZAgn.jpg?1]
We don't know if tetration has changes of state as the base converges to zero, but can only be equal to 0 or 1, so the doubt is how many discontinuities it has on a given interval.

Base -1:
, so, once , then the function must be periodically equal to -1:
This is a possible solution:

[Image: Gs1tpK1.jpg?1]
Is not the only solution; it may be displaced to the right by any real value d (0<d<1), and still will be a solution valid on the interval -2+d<x.

I wonder if there is a family of continuous solutions, and this one is the evolvent.
I have the result, but I do not yet know how to get it.
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Messages In This Thread
Base -1 - by marraco - 05/21/2015, 06:31 PM
RE: Base -1 - by sheldonison - 05/22/2015, 05:28 AM
RE: Base -1 - by sheldonison - 06/01/2015, 03:46 AM
RE: Base -1 - by marraco - 06/02/2015, 01:08 PM
RE: Base -1 - by sheldonison - 06/02/2015, 05:27 PM

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