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 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. | ||
--[[User:Gottfried Helms|Gottfried Helms]] 06:50, 24 November 2011 (UTC) | --[[User:Gottfried Helms|Gottfried Helms]] 06:50, 24 November 2011 (UTC) | ||
Revision as of 01:51, 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 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.
--Gottfried Helms 06:50, 24 November 2011 (UTC)