What would be 1⁄2 in base 2, or 1⁄5 in base 5? I think that p-adic numbers also make an exception for fractions that contain the base in the denominator.
Ah yeah, what I said was wrong. I was thinking of the completion Qn which is a field (i.e. allows for division by all non-zero members, among other things) iff n is prime. The problem with 10-adics can be seen by checking that …2222 * …5555 = …0000 = 0, so doing the completion has no hope of making it a field.
Ah yeah, what I said was wrong. I was thinking of the completion Qn which is a field (i.e. allows for division by all non-zero members, among other things) iff n is prime. The problem with 10-adics can be seen by checking that …2222 * …5555 = …0000 = 0, so doing the completion has no hope of making it a field.