I had an interesting solution due to binary-operation tunnel vision:
Solution
Represent numbers not as numbers themselves but as their “prime factorization” (generalized to non-rationals as in sqrt(2)=2^(1/2))
[x] = 2^x
and
concat(a, 2^a 3^b …) = a*(3^a 5^b …), right-associative (e.g. [][[]] = concat(1, 2^1) = 1*(3^1) = 3).
I had an interesting solution due to binary-operation tunnel vision:
Solution
Represent numbers not as numbers themselves but as their “prime factorization” (generalized to non-rationals as in sqrt(2)=2^(1/2))
[x] = 2^x
and
concat(a, 2^a 3^b …) = a*(3^a 5^b …), right-associative (e.g. [][[]] = concat(1, 2^1) = 1*(3^1) = 3).