Re: [math-fun] solving linear equations made difficult

For example it shows, as recently discussed here, why binary ...111 = -1 (heh, justifying two's complement arithmetic by analytic continuation?!)

That's also how negative integers are represented as 2-adics. Indeed, one can view the [field?] of 2-adics as a generalisation of two's complement capable of representing rationals (and other things, as well). For example, we can divide ...111 by 111 (decimal 7) to obtain the 2-adic expansion for minus one-seventh: ...001001001001001 and obtain one-seventh by taking the two's complement: ...110110110110111. Sincerely, Adam P. Goucher