Except that's not how bases work. The digits would be of the form e^n. See [1]. Since e is not an integer, its number system uses 3 symbols (0, 1, 2) as 3 is bigger than e. Thus, 20 = 2e^1 + 0e^0 = 5.43656...
I don't know about simplify. Subtracting 1 from the above would yield an irrational number. So certainly not useful for arithmetic. How about for mathematical proofs? Well, any integer above 3 is also irrational. Makes Taylor series annoying. Even mundane things like the factorial would not have a nice representation.
I don't know about simplify. Subtracting 1 from the above would yield an irrational number. So certainly not useful for arithmetic. How about for mathematical proofs? Well, any integer above 3 is also irrational. Makes Taylor series annoying. Even mundane things like the factorial would not have a nice representation.
[1] - https://en.wikipedia.org/wiki/Non-integer_base_of_numeration