3 ms·

> It seems a + b = 1. I've seen this before, and it makes no sense. Is it common to ignore that you are carrying a one?

• nh23423fefe 3y ago
  There isn't some state where you are "carrying the one" and the number is different. Carrying is just an algorithm to canonicalize a number w.r.t. to a radix. consider the natural number 9. it is always equal to (1+1+1+1+1+1+1+1+1+0) but the radix is what determines allowable digits in the representation. in any radix >9 you simply write 9, now consider radix=7 you will compute the fact 9 = 7^1*1 + 1^1*2, which implies the numeral is 12. because 9 = 9 + 0 = 7 + (9 - 7) = 7 + 2 = 10_7 + 2_7 = 12_7 computing coefficients doesn't change a number or a sum.
• svat 3y ago
  Given that a = ···256259918212890625 and b = ···743740081787109376 already they "make no sense" as natural numbers. (And they aren't.) We can define p-adic addition more formally, and "following the usual rule for adding numbers" (giving c = ···000000000000000001) is just serving as useful motivation in the meantime (that's why the author says "it seems"). You can look up the formal addition rule for p-adic integers, but meanwhile if you accept that the sum c=a+b is also going to be a p-adic integer, then you can think about: if c is not ···000000000000000001, what else could it be? (If you pick a certain position, say the 100 trillionth digit from the right, what is that digit of c going to be? Same for any other position other than the rightmost one.) (Another analogy: If you consider that 1.0000 - 0.3333 = 0.6667, and 1.00000 - 0.33333 = 0.66667, etc, when you say 1.00000… - 0.33333… = 0.66666…, do you wonder about “where did the 7” go? Footnote 5 in the post discusses this.)
• Bvlynicole 3y ago
  [dead]