Discontinuous functions examples

[phrances]

can you give me an example of two discontinuous functions at a number a whose sum is not discontinuous at a? thanks!:shy:

 

[Hurkyl]

So your goal is to find

{discontinuous} + {discontinuous} = {continuous}.

I bet you're doing it the hard way: you're trying to pick the two discontinuous functions.

It's much harder to be continuous than it is to be discontinuous -- so you should pick the continuous function first, and then worry about what the discontinuous functions are.

 

[phrances]

we were just asked to show that the sum of 2 discontinuous functions is not always discontinuous...

 

[StatusX]

Think about how the sum of two irrational numbers can be rational. It's a similar idea.

 

[Hurkyl]

If it's not discontinuous at a, then it's continuous at a.