Dear Ivars,
concerning:
y* = |y*|(cos Pi.x + i sin Pi.x)
Supposing |y*| constant, and I am sure that it is not, the yx real projection would then be:
Re[y*] = |y*|. cos Pi.x , with period x = 2.
Nothing goes to infinity and comes back after an infinitesimal length. However, for b < e ^(-e), when x -> +oo the gap netween ysup and yinf does not vanish and become hsup - hinf, producing an indetermination between the two extremes. However, in this model, also the asymptotic value of y*, for x -> +oo, should remain complex. The "yellow zone" or "transition area" would then be the graph of this asymptotic real gap, against b, plotted on the yb plane.
By the way, perhaps you also meant: b < e ^(-e).
But, these is only the product of my imagination. Things could be different. Who knows. But, perhaps, we are annoying the other Participants.
GFR
concerning:
Ivars Wrote:I meant the yx plane where we might "see" the sections of y = b # x = b-tetra-x, for b = const. and of their "envelopes". Real numbers h (hsup, hinf) are the limits, for x -> +oo of these envelopes. These "sections" should show, in my opinion, oscillatory behaviours between the ysup and yinf values detectable for any x = n (integer) even and odd, respectively. They must also show, always according to my point of view, continuous line connections between these up/down points. The pseudo-period should be 2 (I mean: 1 + 1).GFR Wrote:Ivars Wrote:Any 2 points on real axis are connected by a line (curve) which leaves real axis and goes to infinity and returns on next point, infinitesimally close to previous.
What? This has nothing to do with what I am trying to say. Are you joking?
GFR
No... It is my intuitive understanding of continuity. You were talking about sinusoids in real plane connecting h even h odd , or perhaps I misunderstood?
Ivars Wrote:I just took the sinusoids out of real xy plane. Based on the fact that tetration tends to take real numbers away from purely real , why can not h(x) < e^-e when extented to real tetration parameter (so that between n odd and n interger as n-> infinity we have n real such that as z-> infinity but is not integer, x^^z = imaginary or complex?We are not on the same track. What I am just trying to say is that the above-mentioned hypothetical oscillatory connections between the up/down points should be continuous and decreasing and could be represented as the projections of y* (complex y) against x, on the real yx plane. Complex y (y*) would then be representable, qualitatively, by a vector y* = |y*|. e^i.Pi.x , rotating according to an imaginary i.Pi.x angular dimension, giving:
y* = |y*|(cos Pi.x + i sin Pi.x)
Supposing |y*| constant, and I am sure that it is not, the yx real projection would then be:
Re[y*] = |y*|. cos Pi.x , with period x = 2.
Nothing goes to infinity and comes back after an infinitesimal length. However, for b < e ^(-e), when x -> +oo the gap netween ysup and yinf does not vanish and become hsup - hinf, producing an indetermination between the two extremes. However, in this model, also the asymptotic value of y*, for x -> +oo, should remain complex. The "yellow zone" or "transition area" would then be the graph of this asymptotic real gap, against b, plotted on the yb plane.
By the way, perhaps you also meant: b < e ^(-e).
But, these is only the product of my imagination. Things could be different. Who knows. But, perhaps, we are annoying the other Participants.
GFR