Sequence Limit (abstract math)

[FourierX]

Homework Statement

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

prove that

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

Homework Equations

Definition of Limit

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.

 

[CompuChip]

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

 

[HallsofIvy]

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