- #1

- 18

- 0

## Homework Statement

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:

https://www.physicsforums.com/showpost.php?p=1987108&postcount=4

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...