Talk:Superfunction: Difference between revisions
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== Superfunction evaluated *at point t* == | == Superfunction evaluated *at point t* == | ||
I seem to not to become familiar with the concept of Superfunctions. But I understand now at least one reason. If we say "F(z) = f(f(f(...f(t))), where f is evaluated z times" then we obscure, that we evaluate f initially *at the point t*. That means, for each *t* we have another superfunction! So a) we should notice that in the article (I couldn't make the change, don't know why) and change the notation, to something like "F_t(z) = f(f(f(...f(t))), where f is evaluated z times beginning at t". | I seem to not to become familiar with the concept of Superfunctions. But I understand now at least one reason. If we say "F(z) = f(f(f(...f(t))), where f is evaluated z times" then we obscure, that we evaluate f initially *at the point t*. That means, for each *t* we have another superfunction! So a) we should notice that in the article (I couldn't make the change, don't know why) and b) should change the notation, to something like "F_t(z) = f(f(f(...f(t))), where f is evaluated z times beginning at t". | ||
We'll see then, that the range of the "superfunction at some t" is limited to intervals between fixpoints and cannot exceed that intervals by change of the parameter z (as long as z is real). An example is "f(t)=2^t-1 ", whose superfunction if evaluated beginning at any value 0<t<1 cannot exceed this range. | We'll see then, that the range of the "superfunction at some t" is limited to intervals around t between fixpoints and that "F_t(z)" cannot exceed that intervals by change of the parameter z (as long as z is real, there is one option for complex z to step to a neighboured interval). An example is "f(t)=2^t-1 ", whose superfunction -if evaluated beginning at any value "0<t<1" - cannot exceed this range. | ||
--[[User:Gottfried Helms|Gottfried Helms]] 06:50, 24 November 2011 (UTC) | --[[User:Gottfried Helms|Gottfried Helms]] 06:50, 24 November 2011 (UTC) | ||
Latest revision as of 00:54, 24 November 2011
Superfunction evaluated *at point t*
I seem to not to become familiar with the concept of Superfunctions. But I understand now at least one reason. If we say "F(z) = f(f(f(...f(t))), where f is evaluated z times" then we obscure, that we evaluate f initially *at the point t*. That means, for each *t* we have another superfunction! So a) we should notice that in the article (I couldn't make the change, don't know why) and b) should change the notation, to something like "F_t(z) = f(f(f(...f(t))), where f is evaluated z times beginning at t".
We'll see then, that the range of the "superfunction at some t" is limited to intervals around t between fixpoints and that "F_t(z)" cannot exceed that intervals by change of the parameter z (as long as z is real, there is one option for complex z to step to a neighboured interval). An example is "f(t)=2^t-1 ", whose superfunction -if evaluated beginning at any value "0<t<1" - cannot exceed this range.
--Gottfried Helms 06:50, 24 November 2011 (UTC)