# Test Review 5 - limit of a constant sequence

1. Oct 15, 2005

### cmurphy

I need to prove that the limit of a constant sequence converges, using the definition of a limit.

This is what I have:

Let e > 0 be given.
Then |sn - s| < e
But sn = s for all sn, thus
|s - s| < e
|0| < e
0 < e
Thus N can be any number?

2. Oct 15, 2005

### Oxymoron

Your solution is close but not correct. Remember, the definition of a limit involves $\epsilon$ AND $\delta$. There is no mention of a $\delta$ in your proof.

3. Oct 15, 2005

### HallsofIvy

Staff Emeritus
No, Oxymoron, there is NO $\delta$ in the proof of a limit of sequenc! That's only for limit of a function in which the variable is takes on continuous values.

CMurphy, your proof is completely correct: N can be taken to be anything. It really is that easy!

4. Oct 15, 2005

### Oxymoron

Sorry guys, didn't realize it was a sequence. Halls is 100% correct, and so are you colleen. However, if it was a function then you need the delta. I hope you realize that you didnt need the delta because you only have a sequence.

5. Oct 16, 2005

### Muzza

That's a truth "with modification", since the epsilon-delta definition of limits (or continuity) can be formulated using only sequences.

Last edited: Oct 16, 2005