Cauchy sequences and continuity versus uniform continuity

[renjean]

Homework Statement

This isn't really a problem but it is just something I am curious about, I found a theorem stating that you have two metric spaces and f:X --> Y is uniform continuous and (xn) is a cauchy sequence in X then f(xn) is a cauchy sequence in Y.

Homework Equations

This proposition is for uniform continuity but I am wondering if it also holds true for just regular continuity.

 

[Office_Shredder]

Think about f(x)=1/x