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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.

Vince Calder

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