»  Mathematics Magazine

October 1997

  Repeated Power: A Comment in Verse


Another reader, John Derbyshire (Huntington, NY) commented — in the form of a Petrarchan sonnet — on "The limit of x^x^ … ^x as x tends to zero," J. Marshall Ash, this magazine, No. 69 (June 96), as follows:

When x is raised to power of x we see
The first step of an iteration which
Can then be carried on without a glitch
For ever. In the range of powers of e
From minus e itself to e inverted
These endless tottering stairs of shrinking x's
Converge! And yet one question still perplexes:
Beyond that range, what facts can be asserted?
J. Marshall Ash, a scholar from DePaul
Has shown us that, when x is microscopic,
The even steps climb up without a stall
To one; the odd steps, likewise asymptotic,
Decline to zero. Thanks go out from all
For shedding light upon this curious topic.