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## Homework Statement

"For what values of z does [tex]e^{e^x} = 1[/tex] ? If [itex]z_m[/itex] and [itex]z_n[/itex] range over distinct roots of this equation, is the set of distances [itex]d(z_m, z_n)[/itex] bounded away from zero?"

## The Attempt at a Solution

This equation doesn't have any solutions, does it? e

^{w}= 1 only when w = 0. w in this case is e

^{z}, which is never equal to zero. I'm incredibly confused about the second part of the question... I assume [itex]z_m[/itex] and [itex]z_n[/itex] are sequences, but that's all I've got.

At this point, I'm more interested in actually figuring out what the heck the question is asking me than I am in finding the answer. Can anyone help?