Question

3 and 1 is: 4 4) The difference between 4​

Answer 1

Yes and No:

“No” first

If we define difference as the function diff(x,y)=x−ydiff(x,y)=x−y then it’s generally a different result, since

diff(x,y)=diff(y,x)diff(x,y)=diff(y,x) really means x−y=y−xx−y=y−x

and simplifying

x−y=y−xx−y=y−x

2x=2y2x=2y

x=yx=y

boom, in this case they are generally different results and namely diff(x,y)=−diff(y,x)diff(x,y)=−diff(y,x)

Time for “Yes”

If we define difference as the function diff(x,y)=|x−y|diff(x,y)=|x−y| then we see |x−y|=|y−x||x−y|=|y−x| by a well know fact that |u|=|−u||u|=|−u| and u=x−y,y−x=−uu=x−y,y−x=−u so diff(x,y)=|x−y|=|y−x|=diff(y,x)diff(x,y)=|x−y|=|y−x|=diff(y,x)

…

Okay, why different contexts?

Well if you travel dd to work and then dd back home, then you traveled 2d2d total. Your gas mileage cares about that more so than the fact that you ended up where you started, which means 0d0d in terms of displacement.

If you care about displacement, where you start and where you finish, like when keeping financial records… then it’s darn important to note that cc was spent (negative sign) and in a different exchange you made rr (positive sign) because now your net for those exchanges is r−cr−c and the total cash flow (in and out