What does it mean seeing as both Pi and e are both
continuous numbers that when you take the equation:
Does that mean something? Did I stumble upon the meaning of life?
pi^e^pi is a meaningful number. It might be a little clearer with a couple
of brackets though. You could write it (pi)^[e^pi] for example. Not too
surprising that it appears to be irrational, i.e. cannot be written as a
ratio of integers, which is the same thing as saying the digits never
repeat. One can show that every fraction n/d where n and d are integers can
be written as a repeating number. And the converse, every repeating
number -- take for example -- 0.123123123123123... is a rational number i.e.
is the ratio of two integers n/d.
There are a whole bunch of numbers that are irrational, i.e. cannot be
written as a ratio of integers. For example sqrt(2) to mention one example.
It is the solution of the algebraic equation X^2 = 2.
There is another whole class of numbers that never repeat -- called
transcendental numbers -- which like irrational numbers never repeats
digits. But these numbers, like pi or e are not the solution to any
algebraic equation. There is no general "test" by which to determine whether
or not a number is transcendent.
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Update: June 2012