Proving a function is continuous

Problem: Prove using epilson delta definition that is continuous for any real number .

I have the case. I just had some problems with the case. Here's what I got.

Let and choose , then implies that and so . Then and since and and then . Since , then . So .

Thoughts? Corrections?

Re: Proving a function is continuous

Quote:

Originally Posted by

**JSB1917** Problem: Prove using epilson delta definition that

is continuous for any real number

.

I have the

case. I just had some problems with the

case.

Oh, come on. If then everywhere.

Thus implies everywhere.

Re: Proving a function is continuous

Quote:

Originally Posted by

**Plato** Oh, come on. If

then

everywhere.

Thus

implies

everywhere.

Lol, this is the problem with drilling too much rigor into people. They start losing their sense of intuition.