Why bases 0<a<1 don't get love on the forum?

[marraco]

I conjecture that tetration base 0 should be a discontinuous function, alternating between the values 0 and 1, with period 2, and as the base approach zero, the negative axis turns into a real, continuous function.


The derivative must converge to a periodic and alternating Dirac Delta, multiplied by c₁-c₂, and the surface of each "Dirac" must be constant on the positive axis.

That's because there is at least one point in each period with value c₁ and c₂.