Hi,
I know this is an old file, but I've recently gone through and found the following error
1.1.7 - Here the function x*y takes the sum of x and y, then subtracts the greatest integer less than that sum... Basically just takes the fractional part of the sum.
As you note, the identity is clearly 0, as adding 0 to any number does not change the fractional part of the number, but the inverse is not -x , as the set is 0 <= x < 1 , and -x is not in the set unless x=0 ...
Instead the inverse should be 1-x for all x> 0 , so that the sum is 1 (with fractional part 0, aka the identity), and inverse of 0 for x=0 , as the sum is 0 with fractional part 0.
Anyway, thanks for the solutions, they've definitely been helpful for me. I hope my comment is helpful for you
Hi,
I know this is an old file, but I've recently gone through and found the following error
1.1.7 - Here the function x*y takes the sum of x and y, then subtracts the greatest integer less than that sum... Basically just takes the fractional part of the sum.
As you note, the identity is clearly 0, as adding 0 to any number does not change the fractional part of the number, but the inverse is not -x , as the set is 0 <= x < 1 , and -x is not in the set unless x=0 ...
Instead the inverse should be 1-x for all x> 0 , so that the sum is 1 (with fractional part 0, aka the identity), and inverse of 0 for x=0 , as the sum is 0 with fractional part 0.
Anyway, thanks for the solutions, they've definitely been helpful for me. I hope my comment is helpful for you