Technically a base 1 system cannot exist (effectively), because it would mean you were counting from zero (nothing). All base systems for real "math" have to index from null. You couldn't even count using 0, 00, 000, 0000 because how would you know if the first 0 indicated actually zero, or was it the first item? You could only identify it by the absence of all marks, which doesn't work in math or any modern setting.