# Sequence Limit (abstract math)

1. Dec 3, 2008

### FourierX

1. The problem statement, all variables and given/known data

If x_n$$\rightarrow$$ L and y_n $$\rightarrow$$ M

prove that

x_n - y_n $$\rightarrow$$ L-M

2. Relevant equations

Definition of Limit

3. The attempt at a solution

I followed and stayed within the definition of limit of a sequence, but I got 0 for x_n - y_n.

2. Dec 3, 2008

### CompuChip

Can you show us what you did then? Probably your approach is correct but you made a small mistake somewhere.

3. Dec 3, 2008

### HallsofIvy

Staff Emeritus
$|(x_n- y_n)- (L- M)|= |(x_n- L)+ (-y_n+ M)|\le |x_n-L|+ |-y_n+ M|$