Hi Alan,
I think that mathematician already knows this but to say that a number is irrational so therefore, by definition, the digits must go on for ever without a repetitive pattern, offers no explanation of why this is so.
Mathematician is just toying with ideas in a way that I think all mathematicians and potential mathematicians must. Only people with good analytical brains do this.
I think that many/most people just accept everything that they are told - assuming that they are told by a source that they consider credible.