Solve for .

.

Define M such that , then

.

So we would be able to choose .

There is no such that for all , but we can restrict the value of .

If we restrict (i.e. so that )

then

.

Thus .

So set so that we can define to be

.

Now all that's left is to write the proof.

Proof: Let and define . Then if , we have

since

since and

.

Thus .