nomercySomebody who likes knowing what CORDIC is! Wow! My study doesn't seem so pointless after all. :)Your definition of substraction does not match your calculation.You say that 9.(9) - 0.(9) = 9, assuming that 0.(9) - 0.(9) = 0. Like (9 - 0) + 0.(9) - 0.(9) = 9 if you break it into terms.Example:Say the first 0.(9) is 0.99 in your case, or 0.9 + a where a = 0.09I almost agree.
Say the second 0.(9) is 0.9 in your case, or 0.9 + b where b = 0Substituting this in your equation:
(0.9 + a) - (0.9 + b) = a - b = 0.09 - 0 = 0.09a and b is the difference between the assumption that the first 0.(9) is 0.99 and the second 0.(9) is 0.9.The error you made in your assumptions is the error that you will find in the result.
In my first post I have 0.(9) * 10 - 0.(9) = 9.(9) - 0.(9), so it's not the second that's missing a nine, it's the first.
And the error in your post above would not be 0.09, but -0.09.
But basically is right. ;D---------------------------------------------------------------------------------------------------------And in our case the error is nailed flat to -0.000...0009, which is equal to 0 .proof:9.(9) - 0.(9) = 9 + 0.(9) - 0.(9) = 9 . (the first number has one nine less, after the point, than the second)Let's scale it to an integral number. (with the most unusual factor)9 + (∞/∞) * ( 0.(9) - 0.(9) ) = 9 ( both infinitys are the same )=> 9 + (1/∞) * ( 99999...99990 - 99999...99999 ) = 9. (that both numbers got the same length)
=> 9 + (1/∞) * ( -9 ) = 9
=> 9 - (9/∞) = 9 - 9 * (1/∞) = 9( the limit value of (1/∞) is 0 )=> 9 - 9 * 0 = 9 - 0 = 9
=> 9 = 9 ( and the error is gone :D )