what’s the remainder of pi after division by 3 and 3^2? notice how the remainder is the same – i.e. there’s no 3s digit needed. and the same will be true for all higher powers of 3. this is because pi is <3^n for all n > 1. but we failed to express the fractional part of pi. if we extend to the p-adic rationals, we can express it as an infinite expansion but that’s not allowed for p-adics – they can only have a finite number of digits in the part to the right of the radix.
Not sure I understand all of it, but the last part about pi not being algebraic made sense to me, at least! Thanks!
what’s the remainder of pi after division by 3 and 3^2? notice how the remainder is the same – i.e. there’s no 3s digit needed. and the same will be true for all higher powers of 3. this is because pi is <3^n for all n > 1. but we failed to express the fractional part of pi. if we extend to the p-adic rationals, we can express it as an infinite expansion but that’s not allowed for p-adics – they can only have a finite number of digits in the part to the right of the radix.