Albeit this is an older thread, would you be kind enough to expound upon your post? It has always been my experience that any repeating decimal can be proved rational via fundamental algebraic manipulation, i.e., application of "logical laws" within an established framework of undefined terms, axioms, definitions and previously proved theorems. It seems to me that declaring an infinite sum of natural powers equal to a particular rational number by definition is akin to writing into law that no child shall be delivered if the weight of such child exceeds that of the natural mother. Laws and definitions aside, the aforementioned mathematical consequence will occur without permission just as surely as maternal weight in the pre-birth shall not exceed twice that of the post-term mom. Both instances can be assured by proof which (by unintended irony) translates to theorem according to definition of the same. It is the theorem that separates truth from assumption...mathematics from wizardry.
...just a thought
Originally Posted by ThePerfectHacker