It is common practice to take N as a natural number in this definition. Even if you take N as a real number there is no incorrectness in the definition, because from the Archimedean axiom it holds that there exists a natural number(say M) such that M>N.

Correct. Another more compact way of saying that is, you could make the distance between arbitrary small by making N sufficiently large.I was told to think of it as a challenge. What do they mean by that? I can only think of two ways to think of it that way and do not know which is the most logical.

You give me any you want, as small as you want. No matter what, I can always find an in the natural numbers where, for every number bigger than it, the distance from each of the terms of my sequence from is less than your

This is incorrect. If could be made less than all the only value you could take for would be zero, since is any positive number.Or, are you challenging me with an and asking me to show that for any number bigger than your , ( ), the difference between L and is less than all .

You are welcome!I know this question probably seems ridiculous but if I don't understand the easy stuff I won't understand the rest of the material.

Thanks!

James