49 for the ask game! Favorite set of numbers?
I'm partial to the p-adics. I find joy in the fact that in some p-adic number systems, you can write out the digits of √-1 (i).
For example, in the 5-adic number system, i is written as
...12230402222411214341040344341302103044132431212
Is this not really cool?
This only works for primes of the form 4n+1 though (e.g. 5-adics, 13-adics, 17-adics etc), and interestingly, for all of those p-adic number systems, i and -i can't be distinguished. That is, while they're written differently, and one is the negative of the other, there no way to determine which is i and which is -i
i and -i can never be distinguished surely?
In any system where you're defining i to be "a thing that squares to -1" it's always arbitrary which you label "i"
Right yes, but I think my point was more that typically, one writes i as either "√(-1)" or literally just as "i", and one writes -i as either "-√(-1)" or just as "-i". In either situation you can easily match up i with "√(-1)" and -i with "-√(-1)". But there's no easy way to match i or -i with ...44132431212. That is, the p-adic notation is indistinguishable – I was not commenting on the values themselves being indistinguishable, though I don't think I made that very clear in my first post.
