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Ha, what a coincidence. It won't work for decimal 10s complement numbers: For x=10 we get 1 + 10 + 100 + 1000 + 10000 + ... = -1/9 And -1 in a decimal com

• thaumasiotes 13y ago
  > Ha, what a coincidence. > It won't work for decimal 10s complement numbers: I don't get why you say this -- you go on to demonstrate the opposite? This is just the other-side-of-the-decimal-point inverse of the well known 0.9999999... = 1 equality. One of my favorite proofs for 0.9999... being equal to 1 goes like so: imagine subtracting it from 1. You'll get a number which has a 0 at every decimal place: 0.0000000.... Obviously, the number with a 0 in every decimal place is 0 itself. Similarly, if you have your integer represented decimally as a bunch of coefficients (0 <= c < 10) of powers of 10, and all of the coefficients are 9, it's fairly straightforward to see that adding 1 will get you a new number for which all of the coefficients are 0. Since adding 1 to the original number gave us 0, we can treat the original number as -1.
  • jonsen 13y ago
    I don't get why you say this Just a narrative of my own experience thinking this through :-) I thought "OMG" would tell you that, sorry.