Okay, so in general, if I wanted to do a proof to show that some function f(x) is continuous for all x, how do i do that? I mean, general proofs of continuity are easy, but how do you prove it to be continuous for all x in a set?

Printable View

- Nov 12th 2009, 12:36 PMjmoney90question on continuity of functions
Okay, so in general, if I wanted to do a proof to show that some function f(x) is continuous for all x, how do i do that? I mean, general proofs of continuity are easy, but how do you prove it to be continuous for all x in a set?

- Nov 12th 2009, 01:16 PMPlato
- Nov 12th 2009, 02:27 PMjmoney90
- Nov 12th 2009, 02:41 PMPlato
Why do you think that there is anything

*vague*about that method?

You suppose that $\displaystyle c\in S$ and show that $\displaystyle f$ is continious at $\displaystyle c$.

There is absolutely nothing vague about that.

Maybe you don't understand the definition of continuity. Is that it? - Nov 12th 2009, 06:00 PMjmoney90
I guess general was more the word I was looking for. I understand the idea behind continuity: the limit as x approaches some point is the same as that function at some value, and alos how to formally work the definition. The book didn't give any examples of a prooof in which you'd prove continuity of a function in general.