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|