Thank you! This thread is full of people insisting on something wrong because they were taught incorrectly; an irrational number is defined in terms of integer ratios for a reason.

It's not like those people haven't worked with an irrational base before, either! Radians have an irrational base. When we talk about 2π radians, or 1/4π radians, that's exactly what we're doing.

That is not what I meant at all. (My phrasing was unclear. Sorry for the confusion.) Jordi understood what I meant though.

It was unclear; I understand rational numbers to be ratios, and irrationals to be inexpressible as fractions, and I see an almost direct connection between that and digital representation in rational bases, so it seemed deeply confusing to see a consequence of the definition of rationals being refuted. The only way out was an irrational base.