andydude Wrote:Are you talking about replacing the nth tower terminology with the nth tetrate term? Because if that's so, then we could use the term tower for nested exponentials. So its a matter of the following options:
- The nth (homogeneous) tower is \( {}^{n}b \) and a nested exponential is \( a^{b^{c^{\cdot^{\cdot}}}} \).
- The nth tetrate is \( {}^{n}b \), and a (heterogeneous) tower is \( a^{b^{c^{\cdot^{\cdot}}}} \).
Anyone care to vote?
Andrew Robbins
a) "Tower of height n", n'th tetrate (the latter, if context of continuous operation is focused), heterogeneous, leave "nested" for some more special cases (though I have no idea actually)
b) @Jay: top exponent, initial exponent; preferring "initial" to connect to iteration-theory("initial state") and due to the opportunity to be able to better talk about infinite towers and their fixpoints then.
Gottfried
Gottfried Helms, Kassel