It's _true_, but it's not good as a definition, because it's hard to reason about. It drags in all sorts of contingent facts about base-10 representations that

It's _true_, but it's not good as a definition, because it's hard to reason about. It drags in all sorts of contingent facts about base-10 representations that are not usually of interest. The equivalent property, that a number is irrational if it's not equal to m÷n for any integers m and n, is much simpler. So we use that as the definition, and from that simple and intrinsic definition, we prove the _theorem_ that the decimal representation of an irrational number never repeats.