The problem is: Suppose f is a function with the property f(x+y)=f(x)+f(y) for x,y in the reals. suppose f is continuous at 0. show f is continuous everywhere.
I saw this post as an alternative solution that doesn't use epsilon-delta:
But I'm not sure how one would be motivated to set h=x-a...
I know it's a nice step and all that ultimately proves the statement, but what would be the main motivation for this?
NOTE: I understand this solution fully. I just want to know how one is motivated to think this way...