... and (2) f is continuous at a if, for every sequence

such that

, the sequence

converges to

.

I need to prove

. We did the first part in class:

I employ the contrapositive approach. Suppose f does not have property (1) and suppose that

. Now if (1) does not hold, then there is

so that,

,

. When

. So in

there is some

so that

Now I am to my problems: 1)I need to prove that, in fact,

. Let

. I need to find

so that, for

.

I am inclined to let

, but then

might not be an integer. So I am not sure what to do about that. Once I find my

, I simply need to finish the epsilon proof of this part.