No. Pi is *demonstrably* not only irrational, but in fact transcendental. It's not something that is "considered until proven differently", it's something that has *already been proven*.
> using another base, maybe a bijective base or written out as fraction.
Rationality is base-independent. That is, as has been explained repeatedly: whether a number is rational or irrational does not depend on the base that one uses to *represent* the number.
Whether the base-n representation of a RATIONAL number *terminates* or not *does* depend on the value of n: in general, a fraction a/b written in lowest terms has a terminating base-n representation if and only if there is a power of n that is a multiple of b; thus, in decimal notation, the only fractions with terminating base-10 representation are those which, when written in lowest terms, have a denominator of the form 2^r*5^s, with r and s positive integers.
I have no idea what "bijective base" is supposed to mean. But do not confuse properties of the *representation* of a number with properties of the *number*. The quantity of symbols needed to represent a number may depend on the base or on the language being used. But whether the number is rational or not is a property of the number, not of its representation.
-- Arturo Magidin
> > > > I hope you do also realise that 1/3 have none terminating decimal expansion in decimal base. But have no problem terminating in bijective base 3.